VATICAN CITY — Days after the election of Pope Francis, word reached the Vatican press office that the new pontiff was unexpectedly celebrating morning Mass. Other popes had presided over morning services, too, but as the world (and the Vatican press office) would soon realize, Francis did things his own way.

This Mass was offered in the small chapel of the Vatican guesthouse where Francis had chosen to live — not, as in years past, at the ornate Apostolic Palace. His audience was not the cardinals of the Roman Curia, but gardeners, janitors and Vatican office workers. And Francis was not merely presiding, as had Pope John Paul II. He was preaching, without notes, as if he were a simple parish priest.

If one with a big message.

“The church asks all of us to change certain things,” Francis said during one of his morning homilies, as he invoked a Scripture reading from St. Paul. “She asks us to let go of decadent structures — they are useless.”

The symbolism of the morning services, which Francis now holds four times a week, is clear: a humbler papacy, where the pope is foremost a pastor to the flock, not a king. But a humbler papacy hardly means humbler papal ambitions. Francis is not just trying to change the Roman Catholic Church. He seems determined to change the world.

Popes are expected to challenge society. But Francis, 78, who lands in Cuba on Saturday and prepares to arrive in Washington on Tuesday for his first visit to the United States, has achieved a unique global stature in a short time.

His humble persona has made him immensely popular, a smiling figure plunging into crowds at St. Peter’s Square. He speaks in deeply personal terms about people discarded by the global economy, whether refugees drowned at sea or women forced into prostitution. His blistering critiques of environmental destruction have seized the world’s attention.

But he is also an inscrutable tactician whose push to change the church has stirred anxiety and hope — and some skepticism. Many conservatives project their fears onto him. Many liberals assume he is a kindred spirit. Others argue that Francis is less concerned about left or right than he is about reversing the church’s declining popularity in Latin America and beyond.

“Francis is a great showman,” said Rubén Rufino Dri, a longtime critic of Francis and an emeritus professor of the sociology of religion at the University of Buenos Aires. He added, “His repositioning of the church is paternalistic. It is not a strategy for empowering its followers. This is by no means a revolution.”

Francis has not fully revealed his hand. But already his spiritual mission to place the poor at the center of the church has enabled him to thrust it to the center of the global debate on issues such as climate change, migration and the post-2008 rethinking of capitalist economics.

To some degree, the question of how Francis will change the church — and its role in society — misses the point that much change has already occurred. Doctrine is the same, but Francis has changed its emphasis, projecting a merciful, welcoming tone in a church that had been shattered by clerical sexual abuse scandals and identified with theological rigidity. He has emphasized its historic connection to the destitute while sidelining culture war issues. In turn, his geopolitical influence, and that of the church, has risen.

“He does have a good deal of soft power, and it is not only among Catholics,” said Joseph S. Nye Jr., a professor at the Harvard Kennedy School. “Many of the popes have certainly said the words about poverty. But what Francis has been able to do is put a focus on it that isn’t blurred or distracted by other things.”

His visit to the United States will pose a critical test. His papacy has firmly emphasized the “peripheries” — both existentially and geographically — as he has pointedly visited smaller countries like Albania, Sri Lanka, Bosnia, the Philippines, Ecuador and Bolivia. By heading to Washington from Cuba, Francis is repeating his point that the peripheries are connected to the centers of power — and no country more represents elite economic and political power than the United States.

Through gestures and words, Francis has repeatedly challenged elites, inside the church and out. He has attacked an insular Catholic hierarchy for focusing too much on dogma and “spiritual worldliness,” and too little on ordinary people. He has attacked prevailing global economic orthodoxy — the belief that markets and the pursuit of wealth will lift all boats — as a false ideology, inadequate for fully addressing the needs of the poor.

In the United States, Francis’ biting critiques of the excesses of capitalism — if ringing true to many people — have caused discomfort even among some sympathizers and outright disdain from critics, who have called him a Marxist or a Communist. Those who have known Francis for years laugh at those labels, yet they agree that he can be elusive, having refused to be placed neatly inside an ideological box since his early days as a young Jesuit leader in Argentina.

“He delights in confounding categorizations,” said Austen Ivereigh, author of the biography “The Great Reformer: Francis and the Making of a Radical Pope.” “There is a sense in which the elites always want to own him, and he’s always eluding them.”

From the moment he stepped onto the central balcony of St. Peter’s Basilica and greeted the masses after his unexpected election in March 2013, Francis made history as the first Latin American pope. He even told a joke that night about how “his fellow cardinals” had gone to the “end of the world” to find a pope.

It was a lighthearted reminder of the great distance to his native Argentina from the Vatican. But what now seems clear is that Francis was not only telling a joke. The “end of the world” was a metaphor for the slums, and the worldview of the Latin American church that he was bringing to the Vatican.

So to better understand the pope of gardeners and janitors and the poor, it is best to start in Argentina, where the man who would become Francis was named Jorge Mario Bergoglio.

The Archbishop of the Slums

For many Argentines, Jorge Mario Bergoglio (pronounced Ber-GOAL-io) was a mystery. When he became archbishop of Buenos Aires in 1998, he converted the official residence into a hostel for priests and moved into the downtown diocesan office building. He took a small bedroom with a portable heater that he switched on when the building’s heating system automatically shut down on weekends. He often cooked himself meals in a small kitchen.

He avoided the limelight, rarely speaking to the media, and spent little time in the affluent parts of the capital. His predecessor as archbishop had courted Argentina’s political elites (which led to a later corruption scandal), but Archbishop Bergoglio erected a divide. His focus was Argentina’s poor. He created a cadre of priests who worked and lived in the slums of Buenos Aires, and he made regular visits, leading religious processions or saying Mass. Before every Easter, he visited prison inmates or AIDS patients or the elderly.

“His papacy is a clear continuity, above all, in his focus on the poor,” said Father Augusto Zampini Davies, who once worked in the Buenos Aires slum of Bajo Boulogne. “The church — those that appointed him — wanted a change. And they wanted a change from the periphery. But perhaps what some did not predict is that when somebody starts to see the world from the viewpoint of the poorest, he undergoes a profound transformation.”

Francis’ grandparents and his father were immigrants from the Piedmont region of Italy who left for opportunity in Argentina, and also to flee Mussolini’s fascist regime. They were supposed to travel in October 1927 aboard The Principessa Mafalda, an Italian ocean liner, but fortuitously missed the departure: The ship sank. The family took another vessel and arrived in Buenos Aires, where other Italians and Europeans had immigrated. Less than a decade later, Jorge Mario Bergoglio was born.

Jorge’s grandmother Rosa was a dominant influence in his life, teaching him Piedmontese-inflected Italian and imbuing him with a love of literature. Among his favorite novels was Alessandro Manzoni’s Italian classic “I Promessi Sposi,” or “The Betrothed,” which he has read at least three times. Mr. Ivereigh, the biographer, argues that Francis’ vision of the church as a “field hospital” is influenced by the book’s depiction of courageous wartime priests working in a field hospital outside Milan.

As a 16-year-old, Jorge was going to meet friends when he was overcome by an urge to detour into a local basilica in Buenos Aires. “I don’t quite know what happened next,” Cardinal Bergoglio said during a 2012 radio interview with a community station in a Buenos Aires slum. “I felt like someone grabbed me from inside and took me to the confessional.”

The teenager stepped out of the confessional convinced that he would become a priest. And even though his family was deeply Catholic, his mother, Regina, opposed her oldest child entering the priesthood, relenting years later after his Jesuit ordination, when she knelt and asked for his blessing.

Among Catholics, Jesuits are famous as missionaries, intellectuals and educators — and for often being stubbornly independent, skeptical and politically adept. They helped create modern Argentina but were temporarily dissolved in 1773 by Pope Clement XIV in a pivotal moment in Latin American history: Clement sided with European monarchs trying divvy up South America, while the Jesuits sided with the indigenous populations living in independent communities known as reductions.

For Francis, the transformative event of his early priesthood was the Second Vatican Council, the meetings from 1962 to 1965, which stirred sharp internal debates and ended with the church adopting a new openness. Mass could now be celebrated in native languages, not just Latin, and the church resolved to open unprecedented dialogue with members other faiths, including Jews.

But for many Catholics, the council proved deeply unsettling and politically divisive. By the 1970s, the Jesuits were divided, partly over different interpretations on how to achieve social justice, and the number of new priests dropped sharply. In Argentina, several Jesuits had embraced a Marxist-influenced strain of liberation theology, a Latin American movement calling for structural change to help the poor.

At only 36, Father Bergoglio was placed in charge of Argentina’s Jesuits. He would later acknowledge his immaturity for such a position — and his lack of preparation. But he won a loyal following and was praised for replenishing the numbers of new priests.

However, his hard-nosed style also brought him enemies. He would be dogged for decades by accusations that he failed to protect two priests who were kidnapped and tortured by the brutal military government ruling Argentina during the 1970s — allegations that have been challenged by biographers and were later refuted by one of the two priests. Among some Jesuits, he was considered an archconservative.

It would not be the last time someone tried to put him into an ideological box.

‘Dung of the Devil’

On a Tuesday morning this June, Pope Francis stood inside the chapel of the Santa Marta guesthouse and spoke about poverty and the Gospel. There was a four-month waiting list to attend one of his morning services. And Francis still reserves the service mostly for ordinary people, or missionaries, priests and nuns, but Vatican Radio is allowed to transmit excerpts from his message globally.

His message, not surprisingly, often comes back to poverty. Poverty, Francis noted on June 16, is “a word that always embarrasses.” He said it was common to hear complaints that “this priest talks too much about poverty, this bishop speaks of poverty, this Christian, this nun talks about poverty,” adding, “Aren’t they a little Communist, right?”

Francis’ first months as pope were a veritable love-fest: Here was the ordinary-guy pope, paying the bill at the hotel where he stayed before his unexpected election; keeping his plain black shoes instead of red papal slippers; eschewing the papal apartment for rooms in the Vatican guesthouse. He washed the feet of inmates, women and a Muslim. He kissed the head of a grossly disfigured man. He signaled a more welcoming public attitude toward homosexuals by saying, “Who am I to judge?”

Traditionalists grumbled, but Francis had managed, seemingly overnight, to rebrand the church, at least in style. But then the substance started coming, too. He released what amounted to his papal mission statement in November 2013, with the publication of “Evangelii Gaudium,” a sweeping 224-page document that many Catholics received as an optimistic call for a tolerant, joyous Catholicism open to the world, and the world’s poor. But many capitalists were jolted by Francis’ blunt attack on the global economic system as “unjust at its root.”

He expanded the theme last June in his landmark environmental encyclical, “Laudato Si’,” in which he held rich countries most responsible for climate change and obligated them to help poor ones deal with the crisis. Then in a July visit to Bolivia, Francis compared the excesses of capitalism to the “dung of the devil” and apologized for the church’s role in Spanish colonialism in Latin America, warning of the “new colonialism” of materialism, inequality and exploitation.

“Once capital becomes an idol and guides people’s decisions, once greed for money presides over the entire socioeconomic system, it ruins society, it condemns and enslaves men and women, it destroys human fraternity, it sets people against one another and, as we clearly see, it even puts at risk our common home,” one of Francis’ speeches in Bolivia asserted.

To some conservatives in the United States, the Argentine pope seems to be making a frontal assault on the American way. Rush Limbaugh blasted him as a Marxist. Others labeled him a communist or socialist. Some affluent Catholic donors withdrew pledges or expressed discomfort.

“I hope I’m not going to get castigated for saying this by my priest back home, but I don’t get economic policy from my bishops or my cardinals or my pope,” Jeb Bush, a Republican presidential candidate and a Catholic, said in response to the environmental encyclical.

The labels rang false to many who knew Francis in Argentina. In Buenos Aires, Francis sharply criticized Marxism, especially as some priests sought to intermingle the dialectics of violent class struggle with the social justice goals of Catholic teaching. Later, he sharply criticized the neo-liberal belief that market economics were a cure-all for the poor.

“He is very critical of ideology because ideologies come from intellectuals and politicians who want to manipulate the hearts of the people,” said Guzmán Carriquiry Lecour, secretary of the Pontifical Commission for Latin America and a longtime friend of the pope. “For him, ideologies hide and defame reality.”

During the 1970s, Francis instead embraced an Argentine derivation of liberation theology, which was known as the theology of the people. It focused on native culture and Argentine traditions, an implicit rejection of the colonialist legacy. Faith derived from the poor, the theology argued, and the poor were central to Christianity. Unlike systems contrived by elites or intellectuals, the Gospel was for everyone.

“They didn’t want to use liberal or Marxist lenses, so they looked for another type of theory to explain Latin American and Argentine society by looking to our history,” said Father Juan Carlos Scannone, an Argentine Jesuit and prominent proponent of the theology. “I wouldn’t say that Francis is a people’s theologian, but he has certainly been strongly influenced by it.”

Economic upheaval has convulsed Argentina for much of the past century. As a child, Francis grew up knowing that his grandparents and other relatives in Argentina had been deeply affected by the global ripples of the 1929 stock market crash and the Great Depression. During Francis’ childhood in the 1940s, Argentina’s Catholic Church was nationalistic and closely identified with the political movement known as Perónism, after Gen. Juan Domingo Perón.

Over decades, Perónism would mutate, blending populism, authoritarianism and nationalism, with Perón ultimately splitting from the Catholic Church. As a young priest during the military dictatorship in 1971, Francis ministered to the Iron Guard, a worker-based social justice group working for the return of Perón, who had been exiled to Spain.

Mr. Ivereigh, the biographer, argues that Francis eventually rejected political ideologies and focused on the pueblo fiel — the faithful — while becoming increasingly outspoken against politicians, whom he thought did too little for the poor. As archbishop of Buenos Aires, Francis mobilized the church in response to Argentina’s economic crisis of 2001-02, expanding the number of priests assigned to the slums, opening food kitchens and opening schools, clinics and drug rehab centers as state services receded.

He also castigated Argentina’s political leaders during the traditional Te Deum service, often with the president in attendance. (The service coincides with Argentina’s anniversary of the May Revolution, a precursor to national independence.)

His rebukes would infuriate different leaders, including former President Néstor Kirchner. His critics argued that he was interfering in secular affairs and playing his own political games.

“He takes risks,” said Rabbi Abraham Skorka, a Jewish leader in Buenos Aires and a close friend to the pope. “He doesn’t stay in a comfortable position.”

Archbishop Marcelo Sánchez Sorondo, an Argentine who has served in the Vatican for more than 40 years, said Francis is not condemning capitalism in total, but he is criticizing the indifference it fosters toward the poor.

“The pope, of course, doesn’t have a solution — the economic solution,” said Monsignor Sánchez Sorondo, who is chancellor of the Pontifical Academy of Sciences. “But the pope is like a light on the street to say: ‘This is not the way. This way sacrifices many people and leaves many people excluded.’”

He added, “The pope is concerned that the plutocracy is destroying democracy.”

Ken Hackett, the United States ambassador to the Holy See, argues that Francis’ economic views have been wrongly simplified and scoffs at the suggestion that the pope is a socialist as “a naïve characterization.”

Mr. Hackett added: “I don’t think he hates capitalism. I think he hates the excesses.”

To a degree, Francis seems to be lashing out against the contemporary primacy of economics over faith. He believes the answers are found with the Gospel, not with Adam Smith or Karl Marx.

‘Europe Was Over’

Inside the grandiose marble nave of St. Peter’s Basilica, the Vatican hierarchy seemed neatly aligned as Francis celebrated his first World Day of Prayer for the Care of Creation on Sept. 1. Cardinals sat in the front rows, draped in red, followed by the bishops in purple. Priests and missionaries came next, and then pilgrims and tourists. In front of Bernini’s iconic baldacchino altarpiece, a priest slowly swung a censer, sending puffs of incense into the air.

Francis sat on a white chair on a raised burgundy dais, while a Capuchin monk offered a homily on the environment. As tourists pointed cellphones at the altar, the ritual, grandeur and continuity of the service — and the sheer weight of gold leaf and marble in the basilica — seemed to make a mockery of Francis’ goal to create “a poor church of the poor.”

His fellow cardinals elected Francis partly because they wanted him to put the Vatican in order after the scandals and bureaucratic dysfunction that preceded the stunning resignation of his predecessor, Pope Benedict XVI, in February 2013.

Since then, Francis has devolved some powers outside the Vatican to a de facto cabinet of nine cardinals from around the world, known as the C9. He has appointed the blunt-spoken Australian George Pell to lead a new economy secretariat charged with putting Vatican finances in order. He has created a new commission to address the clerical sexual abuse crisis. Another panel has helped formulate the recent reforms to Catholic rules on marriage annulments. And still another commission has been charged with modernizing and consolidating the Vatican’s sprawling communications operations.

However, Francis’ reforms are incomplete, and many advocates for sex-abuse victims say he has still failed to fully confront the crisis. But the change he speaks about most often is the one stirring the most resistance: reshaping the pastoral approach of the church and the application of church doctrine.

“The doctrine has to evolve over time, or it is not doctrine,” said Father Humberto Miguel Yañez, a Jesuit moral theologian at Pontifical Gregorian University in Rome and a former Bergoglio protégé in Argentina. “The doctrine is the transmission of the Gospel. To transmit the Gospel, you have to get in touch with contemporary culture. Every era has its own problems. Things don’t stay the same.”

Internal church warfare hews to a language of its own, and many reformers hope that Francis’ repeated emphasis of themes like “mercy” and “openness” signals that he is preparing to redirect Catholic teaching on gays, the divorced and remarried, unmarried couples and other divisive social issues.

No one doubts that an ideological struggle is underway over what constitutes “family,” which is the subject of a major Vatican meeting, known as a synod, in October. An earlier meeting of cardinals grew contentious as factions argued sharply about how accommodating the church should be. Conservatives suspicious that the Argentine pope wants to water down doctrine are still pushing back. Last Tuesday, 11 cardinals published a book in the United States warning that the church should not dilute its rules prohibiting divorced and remarried Catholics from receiving communion.

This year, Cardinal Gerhard Ludwig Müller, who is the Vatican’s doctrinal enforcer as prefect of the Congregation for the Doctrine of the Faith, told a French Catholic newspaper that his office would expand its writ “to provide theological structure” to the papacy because Francis was more a pastor than a theologian. Many interpreted his comments not only as patronizing, but also as an open attempt to rein in the Argentine pope.

Conservatives in the United States have been especially outspoken, led by Cardinal Raymond Burke of Wisconsin, who has been sidelined by Francis. Meanwhile, the German newspaper Die Zeit recently reported that some Vatican officials are circulating a seven-page dossier detailing frustration and anger over the reforms enacted this month by Francis to make the process of obtaining an annulment faster and simpler. The officials accuse the pope of diluting dogma and creating a “Catholic divorce.”

Francis has always had enemies in Argentina and at the Vatican, including some who sought to discredit him during the 2005 conclave in which he finished second to Benedict in the selection of a new pope. But many analysts and Vatican officials say the current friction is also about institutional change — and the deliberate ambiguity of a pope who has created new structures even as many of the old ones remain in place.

“Those who might have considered themselves insiders in the previous regime don’t know how the new one is functioning,” said one senior Vatican official who declined to be identified because he was not authorized to speak publicly. “For the pope, it is a way of keeping his own autonomy. People just don’t know where he’s coming from, or who his closest advisers are.”

After Benedict’s resignation, many pundits predicted the election of a pope from Latin America, home to 40 percent of the world’s Catholics. But doing so has meant more than checking a demographic box. Francis arrived bearing the worldview of a Latin American church that, over recent decades, had developed its own brand of Catholicism.

That vision was expressed most clearly in 2007, when Latin American bishops met at a Marian shrine in Aparecida, Brazil. There, they produced an agenda to evangelize in the streets; to prioritize migrants, the poor, the sick and those on society’s margins; to embrace popular religion, or how ordinary people worship; and to promote environmental protection.

The chief editor of the document? Francis. He would take the “Aparecida Document” with him to Rome as a blueprint for his papacy.

“Europe was over,” said Vincenzo Paglia, head of the Pontifical Council for the Family. “It had no more energy, not even to produce a pope. That is why the pope could only come from Latin America. Not from Africa, not from Asia — they weren’t ready yet.”

The Mona Lisa

Francis is practicing his English. Friends, diplomats and others say he has written his address to Congress and is concentrating on the delivery. He speaks native Spanish, fluent Italian and is conversant in German and French, but friends say he is uncomfortable speaking English. Yet he does not want his pronunciation to interfere with his message, so he is practicing.

“He is aware of the importance of this trip,” Monsignor Paglia said. “He is getting ready, with an extreme zeal.”

The United States is preparing, too. Activist groups promoting different social causes have been going to Philadelphia in advance of Francis’ appearance. Panels have been convened in Washington and elsewhere to plumb the Francis agenda, the Francis psyche, the “Francis Effect.”

In Argentina, some people still struggle to recognize the joyous Francis at St. Peter’s Square as the same seemingly dour man who once led the church in Buenos Aires. There, he kept a deliberately low profile and avoided the news media, other than a handful of trusted journalists. As a young Jesuit, Archbishop Bergoglio was known for his “pious long face,” according to Mr. Ivereigh’s biography. He was sometimes called “La Gioconda,” after the Mona Lisa and her enigmatic smile.

“In some ways, such as his relationship with the media, or his smile, he has changed a bit,” said Father Yañez, the moral theologian. “But I see the same person and the same coherence.”

Francis has blamed himself for some past conflicts in Argentina, especially with his fellow Jesuits (with whom he has reconciled as pope). In a lengthy 2013 interview with Father Antonio Spadaro, a Jesuit, Francis said his “authoritarian and quick manner of making decisions” as a young Jesuit led him to being wrongly labeled an ultraconservative. “I’ve never been a right-winger,” he added, in the interview that was published in Jesuit magazines around the world.

But he is hardly a left-winger, either — at least in the political context of the United States. Even as some of his social and economic views have inspired the American left, he strongly opposes abortion and believes marriage should be between a man and a woman.

“People project their aspirations onto him,” the senior Vatican official said. “Some people might have hopes raised that are not going to be fully realized. For some people, there might be an expectation that there might be a lot of institutional change on things like gay marriage or ordination of women.”

Francis does not seem to mind the contradictions, or even regard them as such. He has encouraged open discussion — even criticism — in advance of the synod in October. He seems determined to open up the church, yet he has not disclosed the exact path he wants the church to follow.

But everyone who knows him agrees that Francis, ultimately, will make a decision. Then the popular, enigmatic pope will show his hand.