“It’s definitely not a progressive agenda,” Mr. Brisport said. “It’s the Mayor Adams agenda.”

Mr. Adams’s supporters contend that despite the mayor’s aggressive stance on law enforcement issues, he has much in common with the progressive wing of the party, noting planned investments in public housing, child care and mental health services.

They also note that Mr. Adams just won an election, and thus has a mandate to lead as he sees fit.

Even before his inauguration, Mr. Adams had struck a defiant tone with left-wingers, rebuffing incoming City Council members by saying he would ignore a written plea to end solitary confinement at Rikers Island. “Like it or not,” he said, “I’m the mayor.”

Evan Thies, an adviser to Mr. Adams, said that “it’s important to recognize that the mayor and many of those who are critical of him from the far left started in the same place” — as working-class New Yorkers, often from “underserved communities” — and want the same things, including equality, affordability, and “a higher quality of life.”

“So his message to them is: We are prioritizing the same people,” Mr. Thies said. “Let’s start there and then talk short-term and long-term solutions.”

Mr. Adams, who at 61 is nearly twice the congresswoman’s age, is a product of a classic New York City political upbringing. Fashioned in the trenches of Brooklyn machine politics, he likes to communicate via street corner interviews and tabloid headlines, something he has managed to regularly generate with a series of nights on the town, trumpeting his swagger as a selling point.

And while his administration uses Twitter as a way to amplify policy and city announcements, the mayor has made clear his disdain for the medium, telling a primary night crowd that “social media does not pick a candidate.”

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