HOLLIS, N.H. (AP) — Florida Gov. Ron DeSantis and former President Donald Trump traded barbs on Tuesday as the two leading Republican White House candidates staged 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 in his first term while pledging to tear down Washington's traditional power centers in ways that Trump fell short.

Speaking later at a Republican women's luncheon in the state capital of 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 his traditional, free-wheeling speech for more than hour but didn't take questions. 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.

DeSantis, asked about people who had twice voted for Trump over his promises to “drain the swamp,” 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 the nation’s capital by instructing Cabinet agencies to halve the number of employees there.

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.”

At his own event, Trump noted that DeSantis is “holding an event right now to compete with us.” Trump vowed to “drain the swamp once and for all” but used the slogan more to criticize President Joe 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 echoed DeSantis 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, as Congress was meeting to certify Biden's 2020 victory, and responded, “If it’s about relitigating things that happened two or three years ago, we’re going to lose."

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

That, too, contrasted with Trump, who repeated baseless claims Tuesday that he was denied a second term because the other side “cheated.” 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 simultaneous visits by the candidates intensified the scrutiny of 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.

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 dominance in the party. But his Democratic rivals ended up winning the state in both the 2016 and 2020 general elections.

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

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 lunch gathering. It complained that DeSantis' event is “an attempt to steal focus from” its own lunch, and that other presidential candidates scheduled around it.

That didn't stop DeSantis from using his town hall to talk 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."

DeSantis' immigration plan was the first major policy rollout of his campaign and calls for ending birthright citizenship, finishing the border wall and sending U.S. forces into Mexico to combat drug cartels. Many of those largely mirror Trump’s policies, while facing long odds since they'd require reversing legal precedents, approval from other countries or even amending the U.S. Constitution.

But the Florida governor also tailored his Tuesday message to New Hampshire, noting how tougher border security could eventually help limit the ravages of opioids, 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,” adding, ”We have to do it because it will save lives.”

DeSantis has tried to gain ground on Trump by questioning the former president's continued hold on the national party. At the town hall, the governor slammed the GOP's “culture of losing” under Trump and mentioned the “massive red wave” that many top Republicans 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.”