“It really represents the excitement that I saw on the streets all throughout the City of New York,” said Letitia James, the New York attorney general. “I haven’t seen this since Barack Obama ran for president of these United States.”

That Mr. Mamdani had such success while running on a far-left agenda, including positions that once were politically risky in New York — like describing Israel’s actions in Gaza as genocide and calling for new taxes on business — may challenge the boundaries of party orthodoxy and unnerve national Democratic leaders.

His views on Israel are likely to force some national Democrats into an uncomfortable position, said David Axelrod, a native New Yorker and Mr. Obama’s chief strategist. But he said that Mr. Mamdani’s relentless focus on economic affordability resonated widely and could be a playbook for the party’s success as well.

“There is no doubt that Trump and Republicans will try and seize on him as a kind of exemplar of what the Democratic Party stands for,” Mr. Axelrod said. “The thing is, he seems both principled and agile and deft enough to confront those sort of conventional plays.”

The primary results raised questions about how Democrats on the national level would react. Would they embrace Mr. Mamdani as a next-generation leader of the party who can articulate a resonant economic message in a way that former Vice President Kamala Harris failed to do in November? Or would they distance themselves from his democratic socialist ideas and move more directly toward the center to court independent voters?