New Yorkers have elected young leftist Zohran Mamdani as their next mayor and Democrats won two key state governor races as US voters delivered an early warning to President Donald Trump ahead of 2026's midterms.

The clean sweep of the top contests among several ballots nationwide on Tuesday will boost morale for Democrats bruised by Trump's onslaught since returning to the White House and set alarm bells ringing in Republican circles.

Mamdani's victory came in the face of 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 to supporters.

"In this moment of political darkness, New York will be the light."

The Democratic Party's victories in the governor's races in Virginia and New Jersey suggested a shift in political mood as the country looks to 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 "pollsters" suggesting the Republican defeats were down to the government shutdown and the fact that his own name wasn't on ballots.

House minority leader Hakeem Jeffries said "Democrats are smoking Donald Trump and Republican extremists throughout the country," writing on X that "the Democratic Party is back."

Mamdani, a state lawmaker for New York's Queens borough, appealed to voters by pledging to tackle the soaring cost of living, offering free city bus travel, childcare and city-run grocery stores.

He focused on living costs facing ordinary New Yorkers, building support through his informal personal style, social media savvy and a massive canvassing ground game.

"The next and last stop is City Hall," Mamdani said in a video posted to X after his victory was declared.

The self-described socialist was virtually unknown before his upset victory to secure the Democratic nomination over former governor Andrew Cuomo, who he trounced again on Tuesday.

There was a party atmosphere at Mamdani's election results viewing event for supporters, held at a storied concert venue in Brooklyn.

Trump made an eleventh-hour intervention in the race, calling Mamdani -- who will become New York's first Muslim mayor when he takes office in January -- a "Jew hater."

Republican candidate Curtis Sliwa, founder of the Guardian Angels citizen crime patrol group, came in third after weeks of Cuomo insisting he bow out to increase his chances.

More than two million New Yorkers cast ballots in the contest, the largest turnout in a mayoral race in more than 50 years, according to the city’s Board of Elections. (AP)