That was according to Edison Research projections as polls began to close.

The victory further cements Trump's dominance over the party as he heads towards a likely November rematch with Democratic President Joe Biden.

"You know, we won New Hampshire three times now, three, three. And we win it every time. We win the primary, we win the generals, we've won it. And it's a very, very special place to me, it's very important."

"And just a little note to Nikki. She's not going to win. She's not going to win."

Trump's only remaining rival in the race, former UN Ambassador Nikki Haley, told her supporters Tuesday night she would remain in the race.

"This race is far from over. There are dozens of states left to go."

With around three quarters of the expected vote counted, Edison showed Trump had close to 54% compared with 44% for Haley.

New Hampshire's primary is 'semi-open', meaning people not registered with any party could still participate in the GOP vote.

Haley had hoped the Northeastern state's sizable bloc of independent voters would carry her to an upset win that might loosen Trump's grip on the Republican Party.

Trump will instead become the first Republican to sweep competitive votes in both Iowa and New Hampshire since 1976.

The results will likely increase calls from some Republicans for Haley to drop out of the race, though her campaign vowed in a memo on Tuesday to push forward until "Super Tuesday," when Republicans in 15 states vote on the same day in early March.

The next Republican primary contest is scheduled for February 24 in South Carolina, where Haley was born and served two terms as governor.

But despite those ties, Trump has racked up endorsements from most of the state's prominent Republicans, and opinion polls show him with a wide lead.