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President Obama visited residents of the rebuilt Tremé area of New Orleans for the 10th anniversary of the hurricane.Credit Doug Mills/The New York Times

NEW ORLEANS — President Obama came to this once-stricken city on Thursday to make a case for his entire presidency: that when disaster strikes, the federal government should help not only to rescue the stranded but also to rebuild better and fairer than before.

“The project of rebuilding here wasn’t just to restore the city as it had been,” Mr. Obama said to several hundred people at a new community center in the once-devastated Lower Ninth Ward. “It was to build a city as it should be — a city where everyone, no matter what they look like, how much money they’ve got, where they come from, where they’re born, has a chance to make it.”

The president explicitly linked New Orleans’s recovery from Hurricane Katrina, which struck 10 years ago this month, to the nation’s recovery from the 2008 recession. “That’s the story of New Orleans, but that’s also the story of America,” he said.

Along with his efforts to change the nation’s health care market, the twin recoveries fit Mr. Obama’s vision of a government that tackles tough problems with bold moves and big investments. To fix the economy early in his presidency, he pushed for an $832 billion stimulus package and a partial takeover of the banking and auto industries. To fix health care, he backed a 1,990-page bill that transformed the business of selling health insurance. And to fix New Orleans, he oversaw a huge, coordinated federal response that invested $71 billion in levees, hospitals and schools.

His Republican critics generally see his efforts as worsening situations, not improving them, so he came to New Orleans to try once again to prove them wrong. Where a timid and delayed response by the Bush administration led to a widely acknowledged disaster, he argued that his own efforts had returned New Orleans not only to its pre-Katrina state but to an even better one. “There’s been a specific process of recovery that is perhaps unique in my lifetime right here in the state of Louisiana, right here in New Orleans,” he said in his speech.

Have all the president’s efforts worked?

Even in New Orleans, that question is hard to answer.

New Orleans’s economy is improving; a new $1.1 billion hospital has opened, and another is being constructed; the school system has been overhauled; and the city is now protected against a “100-year storm” — one that has a 1 percent chance of occurring in any given year — with a $14.5 billion levee system that is far better than its predecessor.

But many of the city’s pre-storm problems, including high levels of poverty and violence, persist. A recent Louisiana State University poll found views of the situation starkly divided along racial lines, with an overwhelming majority of whites saying the region had mostly recovered and a majority of blacks saying it had “mostly not.”

Such racial divides are braided through this city’s history like Creole and jambalaya, a past that Mr. Obama celebrated as he toured a series of new pastel-colored homes in a district, Tremé, that he said was a birthplace of jazz and one of the most important African-American communities in the country.

After holding babies, grinning for pictures and even singing a few bars of the theme song to the television show “The Jeffersons,” Mr. Obama praised the partnerships among every level of government that had rebuilt the area, but acknowledged continuing problems.

10 Years After Katrina The New Orleans of 2015 has been altered, and not just by nature. In some ways, it is booming as never before. In others, it is returning to pre-Katrina realities of poverty and violence, but with a new sense of dislocation for many, too.