Donald Trump has won New Hampshire’s Republican presidential primary election, US media is projecting.

Tuesday’s result further asserts the former US president’s dominance over the party as he heads towards a likely November rematch with Democratic President Joe Biden.

With 14 per cent of the expected vote tallied on Tuesday (local time), according to Edison Research, Trump had 52.3 per cent compared with 46.6 per cent for former UN ambassador Nikki Haley.

The result is a blow to Haley, who had hoped the north-eastern state’s large cadre of independent voters would carry her to an upset win that might loosen Trump’s iron grip on the Republican Party.

In a speech to his supporterse, Trump said it was “a very bad night” for Haley.

“She did very poorly actually,” he said.

“The governor said she’s going to win, she’s going to win, she’s going to win. Then she failed badly.”

Instead, Trump will become the first Republican to sweep competitive votes in both Iowa – where he won by a record-setting margin eight days ago – and New Hampshire since 1976, when the two states cemented their status as the first two nominating contests.

While the final margin was still unclear, the results will likely increase calls from some Republicans for Haley to drop out of the race. Her campaign vowed in a memo earlier on Tuesday to push forward until “Super Tuesday” in early March, when 16 states vote on the same day.

“New Hampshire is first in the nation. It is not the last in the nation. This race is far from over. There are dozens of states left to go. And the next one is my sweet state of South Carolina,” she said after the loss became clear.

South Carolina is where Haley was born and served two terms as governor. Its Republican primary is on February 24.

“Every time I’ve run for office in South Carolina, I’ve beaten the political establishment. They’re lined up against me again. That’s no surprise,” Haley said.

“But South Carolina voters don’t want a coronation. They want an election. And we’re going to give them one.”

Despite that, Trump has racked up endorsements from most of the state’s Republican figures, and opinion polls show him with a wide lead.

Haley also renewed her challenge for Trump to debate her.

Trump chose to respond via his Truth Social media platform, posting that Haley was “DELUSIONAL!!!” as she spoke.

“SHE JUST LOST NEVADA, WHICH IS UP NEXT!” he wrote in another post.

Haley finished third in Iowa, just behind Florida Governor Ron DeSantis. She had focused much of her early campaign on New Hampshire, where the more moderate electorate was expected to offer perhaps her best chance of winning a state over Trump.

New Hampshire was the first contest to feature a one-on-one match-up between Trump and Haley after Florida Governor Ron DeSantis, once seen as Trump’s most formidable challenger, dropped out on Sunday and endorsed Trump.

Despite Trump’s win on Tuesday, however, exit polls hinted at his potential vulnerabilities in a general election campaign.

He faces four sets of criminal charges for a range of offences, including his efforts to overturn his 2020 defeat and his retention of classified documents after leaving the White House in 2021.

Nearly half of the voters who took part in the Republican primary said he would not be fit to serve if convicted in court, according to exit polling by Edison.

A similar number of voters said they did not believe Biden legitimately won the 2020 election, echoing Trump’s false claims that the result was tainted by fraud.

Edison projected Biden would win the New Hampshire Democratic primary.

There were also warning signs for Biden, however. More than two-thirds of Republican primary voters said the economy was either poor or not good, an area where Biden has struggled to highlight his administration’s accomplishments.

Biden is not on the ballot in New Hampshire’s Democratic primary, having supported an effort by his party to move its first primary election to the more diverse state of South Carolina.

New Hampshire supporters were still able to vote for him by writing Biden’s name on the ballot.

The Democratic president, whose advisers expect a rematch with Trump, took aim at Republicans over their efforts curb abortion rights in a Virginia speech on Tuesday.

Biden has also cast Trump as a would-be dictator and a threat to democracy.

Trump, who is balancing campaign stops with appearances in various criminal and civil courts, denies wrongdoing and has used the criminal charges against him to bolster his claim of political persecution.

He predicted victory in New Hampshire early on Tuesday, saying the level of enthusiasm was incredible.

Haley had stepped up her attacks on Trump as the election drew near, criticising his affinity for strongmen such as Russia’s Vladimir Putin and North Korea’s Kim Jong Un.

Haley, 52, has also gone after Trump’s age – he is 77 – and mental acuity, attacks she has also regularly levelled at Biden, who is 81.

“I’ve long called for mental competency tests for politicians over the age of 75,” she said on Tuesday.

“Trump claims he’d do better than me in one of those tests. Maybe he would, maybe he wouldn’t. But if he thinks that, then he should have no problem standing on a debate stage with me.”

-with AAP