US President Donald Trump on Wednesday said the United States had lost "sovereignty" after New Yorkers elected leftist Zohran Mamdani as their next mayor.

"We'll take care of it," Trump said without explaining what he meant, while claiming the country's largest city would become communist.

In a speech in Miami a day after Mamdani's convincing victory, Trump added that the Florida city "will soon be the refuge for those fleeing communism in New York."

"The decision facing all Americans could not be more clear: We have a choice between communism and common sense," he said, also casting the choice as between an "economic nightmare" and an "economic miracle."

Trump later added that he wanted his hometown of New York to be successful and that he might help Mamdani "a little bit, maybe." He did not repeat his threat to withhold federal funding from New York City.

Mamdani's mayoral race win came despite fierce attacks on his policies and Muslim heritage from business elites, conservative media commentators and Trump himself.

Mamdani, who was born in Uganda and became a naturalised American citizen after graduating from college, has cast himself as the embodiment of the resistance against the president, who has pursued an aggressive, anti-immigrant agenda during his second term.

“New York will remain a city of immigrants, a city built by immigrants, powered by immigrants and, as of tonight, led by an immigrant," he said in his election night speech.

“So hear me, President Trump, when I say this: To get to any of us, you will have to get through all of us."

Mamdani spoke about “Trump-proofing” New York City, which he said involves “protecting those with the least from the consequences of a man with the most power in this country.”

But Mamdani said several times that he was willing to work with anyone, including Trump, if they can help New Yorkers. He said he has not heard from the White House or the president following his win.

Mamdani's win, as well as the Democratic Party's other victories in the governor's races in Virginia and New Jersey, suggested a shift in political mood as the country looks towards next year's midterm elections, when control of Congress will be up for grabs.

In another significant win for Democrats, voters in California approved a proposition to redraw electoral districts in a bid to neutralise gerrymandering efforts ordered by Trump in other states.

Trump refused to take any blame for Tuesday's results.

In a post on his Truth Social network, he cited anonymous "pollsters" suggesting the Republican defeats were due to the government shutdown and the fact that his own name wasn't on the ballots. (Agencies)