In a soaring speech on a Queens rooftop in the early minutes of Wednesday morning, Zohran Mamdani, the presumptive winner of the Democratic primary for mayor of New York City, promised to lift up New York City’s working class and serve as a model for the future of his party.

“A life of dignity should not be reserved for a fortunate few,” Mr. Mamdani said. “It should be one that city government guarantees for each and every New Yorker.”

He promised to use his power to “stop masked ICE agents from deporting our neighbors,” vowed to make buses “fast and free” and pledged to freeze the rent on regulated units.

The crowd of hundreds of his supporters, many of them young, clutched cocktails and beers in cups that dripped with condensation as they roared their approval in the midnight heat.

Mr. Mamdani’s apparent victory late Tuesday night represented a sharp rebuke of the Democratic Party establishment and business interests, which largely lined up behind Andrew M. Cuomo, the former governor who resigned in scandal four years ago.

By his account, Mr. Mamdani’s apparent triumph was no mere rebuke of a Cuomo campaign that many had described as joyless and lackluster.