“Comparing him to his predecessor is a little unfair because Mike came from the business community,” said Edward Skyler, an executive at Citigroup and a former deputy mayor under Mr. Bloomberg. “While the mayor has made efforts to engage with business leaders, they are never going to embrace his tax policies.”

From the start, Mr. de Blasio made a point of eschewing the world of Manhattan galas that often bring together the city’s civic and corporate leaders and other markers of the inequality he sought to end. He does not appear in society pages in the manner of Mr. Bloomberg, and, aides say, he would not want to.

“It’s not junior high school. This is not about going to the prom. This is about whether or not people are feeling good about the City of New York as a whole,” said Alicia Glen, a deputy mayor and former Goldman Sachs executive. “I think people would be hard pressed, other than saying, ‘Oh, you know, it would be nice if I saw him at the opera,’ to say anything about the state of New York City.”

She pointed to the East Midtown rezoning as proof of things being done that business supports. “The fact that Pfizer could have sold the building and swanned off to suburban New Jersey but chose actively to reinvest in New York City,” she said. “That to me speaks volumes about how companies are seeing New York City and its future and its present.”

For more than a year, Mr. de Blasio has tried meeting business leaders in a format that better suits him: dinners with his wife, Chirlane McCray, at Gracie Mansion. At first Mr. de Blasio was skeptical, aides said, but he has warmed to the events and held eight such dinners so far. “There is way more common ground than disagreement on the big issues,” said Gabrielle Fialkoff, a senior adviser to Mr. de Blasio who began organizing the dinners in 2016.

While others are eating, Mr. de Blasio delivers remarks about his tenure for much of the meal, then takes questions, according to several people who have attended. One person, who attended a dinner in June, compared the mayor’s speech to a campaign event, but noted that the mayor did not circulate to each table and greet everyone.

“He starts his remarks by saying, ‘I don’t get to hang out with you guys,’” said Robert S. Tucker, the chief executive of T & M Protection Resources, a security firm, who attended a recent dinner. “I walked out of there thinking very differently about him than I did going it.”