"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".

The speech marked the first anniversary of Trump's election victory against Democrat Kamala Harris.

"We rescued our economy, regained our liberty, and together we saved our country on that magnificent night 365 days ago," Trump told his audience of supporters.

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

"If anyone can show a nation betrayed by Donald Trump how to defeat him, it is the city that gave rise to him," Mamdani said in a victory speech late Tuesday.

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 toward 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 neutralize 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.