Donald Trump won the key New Hampshire primary Tuesday, moving him ever closer to locking in the Republican presidential nomination and securing an extraordinary White House rematch with Joe Biden.

With vote counting ongoing, Trump's final margin of victory was unclear, but his sole remaining challenger Nikki Haley was quick to insist she would fight on.

In a rambling victory speech -- loaded with his trademark dark warnings about immigration as he continued to lie about winning the 2020 election -- 77-year-old Trump attacked Haley and said that when the primary contest reaches her home state of South Carolina, "we're going to win easily."

In her own speech, Haley insisted that the race was "far from over" and told supporters that Democrats actually want to run against her former boss, due to his record of sowing "chaos."

"They know Trump is the only Republican in the country who Joe Biden can defeat," Haley, 52, said.

Despite now adding New Hampshire to his previous easy victory in Iowa -- and looking near unstoppable to become the Republican candidate in November -- Trump kept to his hard-right messaging, with no hint of reaching out to the more moderate voters who supported Hailey.

At one point swearing on primetime TV, Trump said the United States was a "failing country" and claimed that undocumented migrants were coming from mental hospitals and prisons, and "killing our country."

Two horse race

With strong turnout in the northeastern state, Haley had hoped for a major upset. But US broadcasters quickly projected her defeat as the first tallies came in.

Trump was already the runaway leader in national Republican polling, despite two impeachments as president, and four criminal trials hanging over him since leaving office.

While Haley repeatedly questioned Trump's mental fitness, her efforts in New Hampshire were not expected to create much more than a speed bump for the populist right-winger's surge to November.

"I think it's a two-person race now between Trump and Biden," Keith Nahigian, a veteran of six presidential campaigns and former member of Trump's transition team, told AFP.

New Hampshire was markedly more Haley-friendly than the states she will subsequently face, should she stay in the race, and continuing into February and South Carolina will be a tough sell.

'Wipeout for Biden'?

Trump won a crushing victory in the first Republican contest in Iowa last week, with Haley a distant third.

What was once a crowded field of 14 candidates then narrowed to a one-on-one matchup on Sunday after Florida Governor Ron DeSantis dropped out, following his second-place Iowa finish. 

No Republican has ever won both opening contests and not ultimately secured the party's nomination.

Trump did little actual campaigning in New Hampshire. However, his message -- a mixture of personal grievance and right-wing culture war firing his base -- has delivered the kind of momentum that supporters believe will sweep him back into the White House.

"I think it's gonna be a wipeout for Biden. He's gone," said Luis Ferre, 72, who traveled from New York to be at Trump's election night party at a Nashua hotel.

Haley spent the week hammering the message, backed by polling, that most Americans do not want to see a Trump-Biden rematch. That, however, may not be enough to prevent the inevitable.

"Nikki Haley's supporters will surely feel that Tuesday night in New Hampshire was a reasonably good night. But once the relative shine of the Granite State result wears off... all but the most ardent Haley supporters will be looking through a glass darkly," said Aron Solomon, a political analyst for legal marketing agency Amplify.

Good night for Biden

Biden, meanwhile, won an unofficial Democratic primary in New Hampshire, giving him a symbolic boost.

The president marked the day by campaigning alongside Vice President Kamala Harris in Virginia at a rally for abortion rights. 

With Trump touting his role in the ending of the constitutional right to abortion, Biden told an enthusiastic crowd that the Republican was "hell-bent" on further restrictions.

After the New Hampshire result came through, the Biden campaign said Trump had "all but locked up" the nomination. 

"The election denying, anti-freedom MAGA movement has completed its takeover of the Republican Party," the campaign said in a statement, referring to Trump's "Make America Great Again" slogan.