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Former President Donald Trump and President Biden don't agree on much — but both say their election rematch is set after convincing wins in New Hampshire's first-in-the-nation primary.

Trump, who faces one remaining primary challenger in former U.N. Ambassador Nikki Haley, claimed an 11-point victory in the Granite State on Tuesday night. In an exclusive interview with Fox News Digital, Trump said he was "very honored by the result" and is "looking forward to going against the worst president in the history of our country." 

Biden said Tuesday the "stakes could not be higher" after winning the New Hampshire primary as a write-in candidate, trouncing Rep. Dean Phillips, D-Minn., who launched a long-shot bid against the incumbent president by arguing Biden is too old and unpopular to win in November. 

"It is now clear that Donald Trump will be the Republican nominee," Biden declared in a statement. "And my message to the country is the stakes could not be higher. Our Democracy. Our personal freedoms — from the right to choose to the right to vote. Our economy — which has seen the strongest recovery in the world since COVID. All are at stake."

2024 NEW HAMPSHIRE PRIMARY RESULTS

Donald Trump and Joe Biden

Former President Donald Trump, left, and President Joe Biden. (FOX News)

Though Trump and Biden may think the race is over, Haley has vowed to stay in and battle Trump in her home state of South Carolina, and perhaps beyond.

"You’ve all heard the chatter among the political class. They’re falling all over themselves saying this race is over. Well, I have news for all of them: New Hampshire is first in the nation. It is not last in the nation. This race is far from over," Nikki Haley told supporters Tuesday at her election night watch party in Manchester, New Hampshire.

Haley, the former governor of South Carolina, is not going down without a fight. She will travel to Charleston on Wednesday for the first in a series of campaign stops in the Palmetto State ahead of the Feb. 24 primary. The campaign announced a new $4 million ad blitz in the state this week, showing every intention of fighting Trump for each delegate.

Speaking to Fox News Digital's Brooke Singman, Trump argued it was time for Haley to suspend her campaign so he could begin targeting Biden with an eye towards the general election in November.

RECORD GOP TURNOUT, CALLS FOR HALEY TO LEAVE RACE ROUND OUT TOP 5 MOMENTS FROM THE NEW HAMPSHIRE PRIMARIES

Trump after New Hampshire win

Republican presidential candidate former President Donald Trump speaks at a primary election night party in Nashua, N.H., Tuesday, Jan. 23, 2024.  (AP Photo/Pablo Martinez Monsivais)

"She should because, otherwise, we have to keep wasting money instead of spending on Biden," the former president emphasized. "If she doesn’t drop out, we have to waste money instead of spending it on Biden, which is our focus." 

Trump's victory in New Hampshire came eight days after he captured a majority of the vote and crushed the competition in Iowa's low-turnout Republican presidential caucuses. And it came two days after Florida Gov. Ron DeSantis suspended his campaign, making the race a two-candidate contest between Trump and Haley.

TRUMP ‘HONORED’ BY NEW HAMPSHIRE WIN, SAYS REPUBLICAN PARTY IS ‘VERY UNITED’

Nikki Haley in New Hampshire

Republican presidential candidate former UN Ambassador Nikki Haley speaks at a New Hampshire primary night rally, in Concord, N.H., Tuesday Jan. 23, 2024.  (AP Photo/Steven Senne)

New Hampshire — where independent voters who make up roughly 40% of the electorate can vote in either major party's contest and have long played an influential role in the state's storied presidential primary — was widely seen as Haley's best chance to stop Trump. 

But Haley came up short, a fact Trump hammered over and over in his victory speech.

He said Haley "ran up to the stage all dressed up nicely" and delivered "a speech like she won. She didn't. She lost." 

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"Let’s not have somebody take a victory when she had a very bad night. She had a very bad night," Trump said.

When asked for a response, a Haley campaign spokesperson referred to her remarks Tuesday night and recent public polling, which suggested Trump would win by as much as 22 points. 

"The political elites never learn. The same naysayers who said Nikki Haley couldn’t defeat a 30-year incumbent state legislator or win the governor’s race in South Carolina are the same people declaring the presidential race over after only two states have voted," said Haley communications director Nachama Soloveichik. "Nikki Haley has never taken her cues from the establishment, and she’s not going to start now. Keep underestimating us — that will be fun."

Fox News Digital's Paul Steinhauser contributed to this report.

Get the latest updates from the 2024 campaign trail, exclusive interviews and more at our Fox News Digital election hub.