By James Oliphant and Gram Slattery

ATKINSON, New Hampshire (Reuters) -Donald Trump and his Republican opponents kicked off a week of campaigning in New Hampshire on Tuesday ahead of the state's nominating contest, with the ex-president's competitors battling to slow his march to the party's White House nomination.

A day after Iowans gave him an overwhelming victory in the first vote of the 2024 presidential contest, Trump, who faces multiple criminal and civil cases, appeared in a New York court to defend himself against charges that he defamed writer E. Jean Carroll after she accused him of raping her decades ago.

More than half of Iowa voters backed Trump, 77, propelling him toward a potentially close and acrimonious rematch against Democratic President Joe Biden, 81, in the campaign for November's presidential election.

Florida Governor Ron DeSantis, 45, finished a distant second to Trump in Iowa, pushing former U.N. Ambassador Nikki Haley, 51, into third.

"We really gotta get back on to Biden and beating the Democrats, and not wasting a lot of time with these two," Trump said of Haley and DeSantis to a crowd of supporters in Atkinson, New Hampshire, located about an hour's drive north of Boston.

Trump is betting he can fast-track the normally months-long Republican selection process with a series of convincing early primary wins to force out his rivals.

Like in Iowa, the candidates face frigid temperatures and snow as they try to turn out supporters to campaign events ahead of the Jan. 23 New Hampshire primary vote.

At a hotel in Bretton Woods, a remote area in New Hampshire's White Mountains, Haley told a group of around 100 supporters who braved a snowstorm that Trump was the wrong choice.

"Rightly or wrongly chaos follows him. You know I’m right," Haley, who held the rally with New Hampshire Governor Chris Sununu, said to cheers.

Desantis spoke at a CNN-moderated town hall at New England College in the town of Henniker, where he said he was encouraged that nearly half of Iowa voters cast ballots for candidates other than Trump.

"(That) tells me that there is an appetite for a different leader," DeSantis said. He held a campaign event earlier on Tuesday in South Carolina, which holds its Republican nominating contest on Feb. 24.

CANCELED DEBATE

With polls showing him far ahead, Trump has refused to debate his Republican rivals. Haley said on Tuesday that she would skip any future party debates unless Trump attends, prompting ABC News to cancel a New Hampshire debate that was set to feature her and DeSantis.

The debate, which had been scheduled for Thursday, was one of two such events scheduled ahead of the New England state's Jan. 23 contest.

"Our intent was to host a debate coming out of the Iowa caucuses, but we always knew that would be contingent on the candidates," an ABC News spokesperson said.

DeSantis had vowed to take the debate stage alone in New Hampshire if necessary. CNN did not respond to a request for comment about its Sunday night debate.

Trump is the only current or former U.S. president to be charged with criminal activity, but he won by an unprecedented margin for an Iowa Republican contest, strengthening his case that his nomination is a foregone conclusion.

He won 51% support in the Midwestern farm state — a victory margin that far surpassed the previous record of 12.8 percentage points for Bob Dole in 1988.

DeSantis won 21% and Haley 19%, with 99% of the expected vote tallied, according to Edison Research. Following the results, entrepreneur Vivek Ramaswamy and former Arkansas Governor Asa Hutchinson both ended their campaigns.

Ramaswamy, who has endorsed Trump, spoke at the former president's campaign event on Tuesday night.

LEGAL WOES

Trump's Iowa triumph showed his enduring popularity among Republicans even after the Jan. 6, 2021, attack on the U.S. Capitol by his supporters and the 91 criminal charges that he tried to overturn the 2020 election, retained classified documents, and falsified records over hush money payments to a porn star.

Trump faces four prosecutions, setting up the unprecedented prospect of a president being convicted or even serving from prison, with the courts almost certainly weighing in at every stage.

The former president claims falsely that his 2020 election loss to Biden was due to widespread fraud and has vowed, if elected again, to punish his political enemies and introduce new tariffs on imports.

Nearly two-thirds of Iowa caucus-goers embraced his false voter fraud claims, saying they did not think Biden legitimately beat Trump. More than 60% said Trump would be fit to serve as president even if convicted of a crime.

He has drawn criticism for increasingly authoritarian language, including comments that undocumented immigrants were "poisoning the blood of our country." He has also vowed to end the almost two-year-old Ukraine-Russia war in 24 hours, without saying how.

Biden used Trump's decisive Iowa win to frame the November election as a battle against "extreme MAGA Republicans," a reference to Trump's Make America Great Again slogan, and urged supporters to donate to his re-election effort.

While Trump's performance in Iowa showed his enduring popularity among Republican voters, it remains unclear how that might translate among a wider swath of the American public in November's general contest.

Iowa and New Hampshire - which are majority white and less populated - historically have played outsized roles in presidential campaigns given their early spots on the campaign calendar. But Democrats have changed their playbook, shifting their initial nominating contests to South Carolina, Nevada and other more densely populated and racially diverse states that they say better reflect the nation.    

A Reuters/Ipsos poll this month found many Americans appear unenthusiastic about their choices so far with Trump and Biden in a dead heat.

Read Reuters' full U.S. election coverage here:

Republicans look to New Hampshire after Trump's landslide Iowa win 49