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Mayor Bill de Blasio at Baruch College in February after his State of Our City address.Credit Damon Winter/The New York Times

New York City mayors have not generally taken kindly to criticism.

Admissions of fault from Michael R. Bloomberg were few. Opponents of Rudolph W. Giuliani were treated to mayoral nicknames like “idiot” or “moron.” Rebuttals to the constituents of Edward I. Koch came, occasionally, in the form of a single digit.

“There were times when he walked up, and some guy was screaming at him,” George Arzt, who was Mr. Koch’s press secretary, recalled. “And Ed would give him the finger.”

So it is with some historical dissonance that certain advocates, elected officials and other self-identified irritants have noted a shift under Mayor Bill de Blasio: He has, at least when it suits him, shown a bit more deference to squeaky wheels.

The instinct has extended to subjects profound and piddling — Mr. de Blasio recently visited the plazas of Times Square, where topless tip-seekers had attracted the attention of the city’s tabloids and led the mayor to order a sweeping review of the area.

Some changes have been subtler than others.

Ding the mayor for persistent tardiness? He has been consistently more punctual at recent public events.

Hit him for avoiding interactions with voters? He has begun taking questions from all comers in radio interviews for the first time in his term, and last Monday he answered questions in an unannounced Twitter chat (though he continues to resist in-the-flesh town-hall-style forums).

Then there was the quarrel with Uber, the car service company. After pushing a plan to cap the company’s growth, Mr. de Blasio abruptly changed course in July amid an aggressive ad campaign against him.

Those close to the mayor are sensitive to any perception that he is too reactive to pressure, from the public or from private interests. They say his only bias is toward good ideas, whether inspired by the pleas of critics or the persuasive powers of his own team.

Supporters argue that his background, as a city councilman and public advocate, has sharpened his attention to constituent services, in contrast to the last two mayors, who lacked such municipal experience.

James Oddo, the Staten Island borough president, recalled some residents’ complaints last spring when Mr. de Blasio, in the midst of a national tour to discuss income inequality, was perceived as having spent little time in the self-described “forgotten borough.”

Soon, mayoral aides arranged a visit for Mr. de Blasio, shovel in hand, to discuss city funding for road repairs.

“The not-coming-to-Staten-Island narrative needed to be ended as quickly as possible, and it’s relatively easy to do,” Mr. Oddo said. “You come to the island.”

Others have noted the risks of appearing too pliable, particularly amid a series of bumps this summer.

“If you’re constantly playing defense, then you’re always reacting and it takes away from the larger vision that you have for the city,” said Christina Greer, a political-science professor at Fordham University. “Don’t over-respond, you know?”

The starkest example, she said, was the hiring of nearly 1,300 police officers as part of a city budget agreement announced in June.

The decision came as the mayor faced pressure over increases in shootings and homicides this year and followed weeks of assurances from Mr. de Blasio that existing staffing levels were sufficient.

City officials have said the hiring was unrelated to the crime statistics, which have since improved. The administration likewise argued that the city’s more prominent discussion of homeless policy of late does not owe to a spate of critical headlines. (Mr. de Blasio announced last week the departure of the deputy mayor overseeing the effort.)

Other course corrections have been easier to trace. These have included a since-amended decision to cut funding for middle school summer programs — “We screwed up,” the mayor said after City Council members objected — and the return of a flag commemorating military service in front of City Hall.

“A stupid mistake,” Mr. de Blasio said of its disappearance, which was covered aggressively by The Daily News. The banner now flies again.

Mr. de Blasio has checked some boxes more discreetly. Teased by some Yankees fans for failing to attend a game during his first year in office, Mr. de Blasio, an avowed Red Sox fan, stopped by the stadium in June before a news conference in the Bronx.

The visit was left off his public schedule. Days later, after pictures with fans had surfaced, a spokeswoman for the Yankees, Alice McGillion, said the team had been unaware of the mayor’s attendance.

Of course, causality in the mayor’s behavior is not always obvious. (His baseball attendance record, after all, includes two games in Milwaukee this year and a recent stretch of four games in five days.)

There have also been several instances in which the mayor has held firm against calls for him to adjust his approach. Perhaps most notable is his defense of “broken windows” policing, despite the protests from some police reform advocates who helped elect him.

But allies have sensed a change in strategy since Peter Ragone, Mr. de Blasio’s former senior adviser, departed this year. Mr. Ragone, who often proudly told reporters that he paid no attention to tabloid coverage, made it known that the administration cared little about day-to-day squabbles and instead focused on what he called “the long view.”

While aides say the administration remains most focused on long-term goals, like an affordable-housing plan, they do not dispute that Mr. de Blasio has at times felt compelled to engage his critics more aggressively.

On Wednesday, after the administration announced reductions in shootings and murders from June through August, City Hall could not resist playing headline writer for a frequent foe.

That evening, the mayor’s Twitter account posted a doctored front page from The New York Post.

“Safest Summer in 20 Years,” the tagline read. “But We Still Hate de Blasio.”