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, it was unclear if Trump had secured the knockout victory to put his sole remaining challenger Nikki Haley out of the contest.

In a speech following the vote, the former UN ambassador during Trump's frequently chaotic presidency said the race was "far from over" and told supporters that Democrats "want" to run against her former boss.

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

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

Donald 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 the 77-year-old's mental fitness and warned another Trump presidency would bring "chaos," polls indicate her efforts in New Hampshire created little more than a speed bump.

"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 states she will subsequently face, should she stay in the race, and continuing into February will be a tough sell without a win or at least a narrow loss.

Her next must-win stop will be her home state South Carolina.

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

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

Donald 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 seemingly insurmountable polling leads.

One of Trump's complaints has been his false claim that Democrats are allowed to vote in the Republican contest in New Hampshire.