With victory all but assured, Mamdani, a 33-year-old democratic socialist who ran an energetic campaign centered on the cost of living, told supporters, “I will be your Democratic nominee for the mayor of New York City.

In the words of Nelson Mandela, ‘It always seems impossible until it is done,’” the democratic socialist said.

Zohran Mamdani, a state assemblyman and democratic socialist, had a commanding lead over former Gov. Andrew M. Cuomo, who conceded in the Democratic primary.