A signature component of the proposed Bloomberg initiative will be a “Mayors Challenge,” through which city executives will be invited to compete for six- and seven-figure grants from Bloomberg Philanthropies, awarded to mayors who draw up compelling proposals for policy experimentation. Mr. Bloomberg’s foundation has run similar competitions in Europe, Latin America and the Caribbean.

Mayor Karen Freeman-Wilson of Gary, Ind., whose city has received money from Mr. Bloomberg’s foundation in the past, said new grants could help address an issue closer to the ground level of government: removing or replacing vacant commercial buildings throughout the city. Ms. Freeman-Wilson said state and federal officials appeared to have little interest in facilitating such actions.

“They don’t have any sense of what we’re confronted with,” she said.

Mr. Bloomberg said the project’s $200 million budget would be spread out over three years, to start with, and could grow over time.

In a reflective aside, Mr. Bloomberg also appeared to acknowledge that he might have more success shifting public opinion on big issues by working through city governments. As a political donor, he has made gun control his central cause, with mixed electoral success, and has also backed campaigns supportive of an immigration overhaul and environmental regulation. Though he is not a member of a political party, Mr. Bloomberg endorsed Hillary Clinton in last year’s presidential race and denounced Mr. Trump at the Democratic National Convention in Philadelphia.

One lesson of that election, Mr. Bloomberg suggested, might be that elites have done too much to change “the moral and social fabric of the country” without explaining the changes to ordinary people.

“I’m certainly as guilty as anybody,” he said. “Maybe that’s one of the lessons of the Trump victory — that we’ve not really talked to lots of people in this country, particularly in the Midwest, where Donald Trump did very well.”

Mr. Bloomberg’s announcement in Miami Beach comes at a pivotal moment for the Conference of Mayors, which faces sky-high and mostly self-imposed political expectations: Many of its prominent members have promised in sweeping language to counteract the influence of the federal government under Mr. Trump.