Gov. Ron DeSantis of Florida on Thursday avoided saying directly that he would endorse Donald J. Trump in 2024 should the former president win the Republican nomination, showing his reluctance to make a benign show of support for the man who is beating him by a wide margin in national polls and insulting him nearly every day.

Asked by a reporter at a news conference in Tampa about whether he would endorse Mr. Trump, the governor responded by complaining that Mr. Trump had recently criticized his policies during the coronavirus pandemic. Mr. DeSantis noted in particular that his rival had compared him unfavorably to New York’s former governor, Andrew M. Cuomo, a Democrat.

“So what I would say is this: When you are saying that Cuomo did better on Covid than Florida did, you are revealing yourself to just be full of it,” Mr. DeSantis said. “Nobody believes that.”

“I remember in 2020 and 2021, when he was praising Florida for being open, saying we did it much better than New York and Michigan and everyone was coming to Florida and that we were one of the great governors in the United States,” he continued, his voice rising. “And he used to say that all the time. Now, all of a sudden, his tune is changing. And I would just tell people, do you find it credible? Do you honestly find it credible?”

Mr. Trump himself has not pledged to back the party’s nominee in 2024 if a rival defeats him in the primaries, underscoring the level of division in the Republican field. Mr. Trump’s federal indictment has led some of the other candidates to more openly criticize him, questioning his judgment. But Mr. Trump, who regularly calls Mr. DeSantis “Ron DeSanctimonious” and accuses him of needing a “personality transplant,” retains the support of many Republican voters.

At the end of his answer, Mr. DeSantis, who is trailing Mr. Trump by roughly 30 percentage points in national polls as more candidates jump into the race, turned to acknowledge the importance of the nominating contest.

“It’s an important process and, you know, you respect the process and you respect the people’s decisions how this goes,” he said. “But I’m very confident that those decisions are going to be positive for us.”

On social media, Mr. Trump’s allies quickly pounced on Mr. DeSantis’s refusal to pledge loyalty to his rival if he falls short.

“Ron DeSantis just proved once again why he’s a Never Trumper in the mold of Liz Cheney and Jeb Bush, completely disqualifying him for 2024, as well as 2028,” Steven Cheung, a spokesman for the Trump campaign, said in a statement.

But Mr. Trump, of course, has taken a similar stance.

“It would depend,” Mr. Trump said in a radio interview earlier this year when asked if he would support “whoever” won the party’s nomination. He added, “It would have to depend on who the nominee was.”

Republicans have generally shown far more grace to Mr. Trump than to his rivals, chastising those challenging the former president for sentiments similar to ones he has also expressed.

The Republican National Committee has said that candidates must promise to support the party’s eventual nominee if they want to participate in debates.

Later on Thursday, at a campaign event in South Carolina, Mr. DeSantis seemed to backtrack slightly, interrupting a reporter who asked why he had seemed to avoid committing to support Mr. Trump.

“I didn’t avoid, no, I was misquoted,” Mr. DeSantis shot back. “Here’s what I said, I said: ‘You run this process. You compete and you respect the outcome of the process.’ And I’ve always said that. And so that’s what I said before. That’s what I’ll do. I think I’m going to be the nominee. No matter what happens, I’m going to work to beat Joe Biden.”

Voters at the South Carolina event said they hoped Mr. DeSantis and other Republican candidates would back Mr. Trump, should the former president be the nominee.

“I think everybody should unite, whoever gets the nomination,” said Shawn Risseeuw, 57, a mechanical engineer who lives in North Augusta, S.C., and described himself as a strong DeSantis supporter. “They’re fools if they don’t.”

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