The former president, who is facing dozens of criminal charges in several court cases, said his challenger Nikki Haley had "a very bad night."
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The former president romped to an easy victory in New Hampshire's primary on Tuesday, as voters picked him over Nikki Haley as their favourite Republican candidate to face Joe Biden in November's presidential election.
With 70% of the votes counted, Trump has a lead of around 10 points: 54% to Haley's 43%.
The result was a setback for Haley, a former American ambassador at the United Nations, who finished second despite investing significant time and financial resources in a state famous for its independent streak.
She's the last major challenger after Florida Governor Ron DeSantis ended his presidential bid over the weekend, allowing her to campaign as the sole alternative to Trump.
Trump’s allies ramped up pressure on Haley to leave the race before the polls had closed, but Haley vowed after the results were announced to continue her campaign. Speaking to supporters, she intensified her criticism of the former president, questioning his mental acuity and pitching herself as a unifying candidate who would usher in generational change.
“This race is far from over. There are dozens of states left to go,” Haley said, while some in the crowd cried, “It’s not over!”
Trump, meanwhile, can now boast of being the first Republican presidential candidate to win open races in Iowa and New Hampshire since both states began leading the election calendar in 1976, a striking sign of how rapidly Republicans have rallied around him to make him their nominee for the third consecutive time.
At his victory party Tuesday night, Trump repeatedly insulted Haley and gave a far angrier speech than after his Iowa victory, when his message was one of Republican unity.
“Let's not have someone take a victory when she had a very bad night,” Trump said. He added, “Just a little note to Nikki: She’s not going to win.”
With easy wins in both early states, Trump is demonstrating an ability to unite the GOP’s factions firmly behind him. He’s garnered support from the evangelical conservatives who are influential in Iowa and New Hampshire’s more moderate voters, strength he hopes to replicate during the general election.
Trump posted especially strong results in the state's most conservative areas, while Haley won more liberal parts. The only areas in which Haley was leading Trump were in Democratic-leaning cities and towns such as Concord, Keene and Portsmouth.
About half of GOP primary voters said they are very or somewhat concerned that Trump is too extreme to win the general election, according to an Associate Press survey of the state’s electorate. Only about one-third say the same about Haley.