At his own party in Nashua, Trump opened his speech by mocking Haley, calling her an "imposter" and saying, "She's doing, like, a speech like she won. She didn't win. She lost. ... She had a very bad night."

His remarks followed a series of angry posts on his Truth Social app, calling her "DELUSIONAL".

Haley had hoped the northeastern 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.

Instead, Trump will become the first Republican to sweep competitive votes in both Iowa - where he won by a record margin eight days ago - and New Hampshire since 1976.

With 41 per cent of the expected vote tallied, according to Edison, Trump held a comfortable 54.7 per cent to 43.7 per cent lead.

While the final margin was still unclear, the result will likely bolster some Republicans' calls for Haley to drop out of the race and allow the party to coalesce behind Trump.

Her campaign vowed earlier on Tuesday to push forward until "Super Tuesday" in early March, when Republicans in 15 states and one territory vote on the same day.

The next competitive contest is on February 24 in South Carolina, where Haley was born and served two terms as governor.

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

In Iowa, Haley finished just behind the second-place Florida Governor Ron DeSantis while focusing 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.

DeSantis, once seen as Trump's most formidable challenger, dropped out on Sunday and endorsed Trump.

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

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.

About 44 per cent of Republican primary voters said he would not be fit to serve if convicted in court, according to Edison's exit polling.

More than half 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 based on write-in votes after he declined to appear on the ballot, having supported his party's effort to move their first primary election to South Carolina.

.With 18 per cent of the estimated vote counted, Edison said Biden had 66.8 per cent, far ahead of US Representative Dean Phillips at 20 per cent.

There were warning signs for Biden, however. Nearly three-quarters 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.

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.

Haley had stepped up her attacks on Trump as the election drew near, criticising his affinity for strongmen such as Russia's Vladimir Putin.

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.

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