Republican presidential candidate Florida Gov. Ron DeSantis during a town hall event on Tuesday in Hollis, N.H. He pledged to tear down Washington’s traditional power centers and build the U.S-Mexico border wall. Josh Reynolds/Associated Press

HOLLIS, N.H. — The rivalry between Florida Gov. Ron DeSantis and former President Donald Trump deepened Tuesday as the two leading Republican White House candidates mocked each other during dueling events in the critical early voting state of New Hampshire.

Addressing a town hall in Hollis, DeSantis vowed to “actually” build the U.S.-Mexico border wall that Trump tried but failed to complete as president. He also pledged to tear down Washington’s traditional power centers in ways that Trump fell short.

Speaking later at a Republican women’s luncheon in Concord, Trump countered that DeSantis was being forced to settle for second place in the primary and accused the governor of supporting cuts to Social Security, Medicare and other entitlement programs as a way to tame federal spending.

Beyond the rhetoric, the conflicting events demonstrated each candidate’s evolving strategy. DeSantis took extensive audience questions – a trademark in New Hampshire politics that he eschewed during his previous visit to the state, drawing criticisms that he was stilted and overly scripted.

Trump, meanwhile, offered a free-wheeling speech for more than hour. He didn’t take questions in Concord, and reporters covering the event were confined to a pen, chaperoned to the bathroom and told they could not speak to attendees in the conference center ballroom or even in the hallways. But the former president answered questions at a subsequent stop in Manchester, where he opened his New Hampshire campaign office.

DeSantis, asked about people who had twice voted for Trump because of his promises to “drain the swamp” in Washington, used his answer to draw some of his sharpest contrasts yet with the former president.

“He didn’t drain it. It’s worse today than it’s ever been,” DeSantis said. He added that such promises don’t go far enough because a subsequent president “can just refill it.”

“I want to break the swamp,” DeSantis said, pledging to take power out of Washington by instructing Cabinet agencies to halve the number of employees there.

DeSantis has tried to gain ground on Trump by questioning the former president’s continued hold on the national Republican party. At his town hall, the governor slammed the GOP’s “culture of losing” under Trump and mentioned the “massive red wave” that many in the GOP predicted but that never materialized nationally in last year’s midterm elections.

“We had a red wave in Florida,” DeSantis said, noting he easily won reelection last fall. “But that’s because we delivered results in Florida.”

Many leading Republicans remain fiercely loyal to Trump, but there is some evidence that the attacks against the former president are resonating. Speaking about Trump on Tuesday, House Speaker Kevin McCarthy, a California Republican, said, “Can he win that election? Yeah, he can win that election.”

“The question is, is he the strongest to win the election?” McCarthy continued on CNBC’s “Squawk Box.” “I don’t know that answer.” He clarified later in the day to the conservative news outlet Breitbart that Trump “is stronger today than he was in 2016.”

In his own speech, Trump noted that polls show him with large primary leads. He seized on DeSantis saying that, while Social Security and other programs need to be guaranteed for older adults, there may be work “in a bipartisan way to figure out how do you strengthen this” when it comes to younger people.

“You can bet he’ll be doing it later,” Trump said of cuts to the programs. “And he’ll be doing it to you.”

Trump also vowed to “drain the swamp once and for all” but used the slogan more to criticize President Biden than the Florida governor.

“You can’t drain the swamp if you’re part of the swamp, and Joe Biden and other opponents, many of them, are all owned, controlled, bought and paid for, 100%,” Trump said.

The former president also largely echoed DeSantis’ sentiments in promising that “this election will be the end of the world for the corrupt political class in our nation’s capital.”

DeSantis was also asked about the pro-Trump mob that overran the U.S. Capitol in January 2021, and responded, “If it’s about relitigating things that happened two or three years ago, we’re going to lose.”

“I had nothing to do with what happened that day. Obviously, I didn’t enjoy seeing it,” DeSantis said. “But we’ve got to go forward on this stuff. We cannot be looking backwards.”

That, too, clashed with Trump, who repeated baseless claims Tuesday that he was denied a second term by election fraud. Numerous federal and local officials, a long list of courts, top former campaign staffers and even Trump’s own attorney general have all said there is no evidence of the fraud he alleges.

The candidates’ simultaneous visits highlighted the role that New Hampshire, the first-in-the-nation GOP primary state, will play in deciding the next Republican presidential nominee. Much of the focus of the early primary has been on Iowa and South Carolina, where evangelical Christians are dominant.

Former President Donald Trump speaks at the New Hampshire Federation of Republican Women Lilac Luncheon on Tuesday in Concord. His first-place finish in New Hampshire’s 2016 Republican primary helped propel him to party dominance. Steven Senne/Associated Press

Spending time in New Hampshire, by contrast, gives the candidates were testing their messages in front of a more libertarian-leaning electorate.

Trump’s first-place finish in New Hampshire’s 2016 Republican primary, after losing Iowa to Texas Sen. Ted Cruz, helped propel him to party dominance. But his Democratic rivals won the state in the 2016 and 2020 general elections.

Before his speech Tuesday, Trump announced that his New Hampshire team features 150-plus dedicated activists and organizers throughout the state’s 10 counties.

Sabrina Antle, from the town of Henniker, said she couldn’t afford to attend the Concord lunch. She and her 9-year-old daughter tried to see the former president later in Manchester, but that event reached capacity before they got in.

“I’m a Trumper but I wouldn’t be upset with Ron DeSantis because I think he’d do a stand up job,” Antle said. “I just don’t know if he has the attitude Trump has, just the assertiveness.”

DeSantis’ campaign angered some members of the New Hampshire Federation of Republican Women by scheduling his town hall around the same time Trump was addressing the group’s luncheon. It called DeSantis’ event “an attempt to steal focus from” its lunch, noting that other presidential candidates scheduled around it.

That didn’t stop DeSantis, who at the town hall talked up the new immigration policy proposal he released Monday in South Texas – betting that the issue can energize GOP voters, even those who are 2,000 miles north of the U.S.-Mexico border.

“We’re actually going to build the wall,” DeSantis said of Trump’s failed pledges to do so. “A lot of politicians chirp. They make grandiose promises and then fail to deliver the actual results. The time for excuses is over. Now is the time to deliver results and finally get the job done.”

But the Florida governor also tailored his Tuesday message to New Hampshire, noting how tougher border security could eventually help limit the ravages of opioid addiction, which have hit the state particularly hard, even as deaths from overdoses have climbed all over the country.

He promised the “most assertive” policy against drug cartels “any administration has ever had.”

”We have to do it,” DeSantis said “because it will save lives.”