GOP presidential front-runner Donald Trump said Tuesday he’s revoking his vow to support the party’s eventual nominee and said he’s freeing Sen. Ted Cruz from his own promise to back Republicans’ candidate.

“He doesn’t have to support me. I really don’t believe I need his support,” Mr. Trump said in a town hall from Wisconsin hosted by CNN.

Minutes earlier, Mr. Cruz had declined to stand by the firm pledge he, Mr. Trump and the rest of the GOP field took last year to back the eventual winner of the primary.

Pressed by host Anderson Cooper, Mr. Cruz said things have changed, and said his goal is now to make sure he doesn’t have to face that choice.

“The answer to that is to beat him at the ballot box,” Mr. Cruz said.

The relationship between the two men has deteriorated dramatically since last year, when pundits said Mr. Cruz appeared to be striking up a “bromance” with the billionaire businessman.

Mr. Cruz said Mr. Trump ruined that when he said in recent days he would go after Mr. Cruz’s wife in retaliation for an anti-Trump super political action committee’s ad featuring a racy picture of his wife, Melania, a former model.

“I’m not an easy person to tick off, but when you go after my wife, when you go after my daughters, that does it,” Mr. Cruz said.

He accused Mr. Trump of being behind a thinly sourced story last week in the National Enquirer tabloid that reported Mr. Cruz had engaged in affairs with a handful of women. The story aggregated rumors, and the only named source was Roger Stone, an adviser to Mr. Trump, who said: “These stories have been swirling around Cruz for some time. I believe where there is smoke there is fire.”

When asked the same question, Ohio Gov. John Kasich said he’d give the same refusal to commit as Mr. Cruz did, adding that maybe it was mistake for all the candidates to have made that pledge in the first debate.

“I gotta see what happens,” Mr. Kasich said. “If the nominee is somebody who I think really is gonna be hurting the country and dividing the country,” he couldn’t endorse him.

When asked by Mr. Cooper if that was a reference to Mr. Trump, the Ohio governor demurred, saying he didn’t want to get more negative.

CNN was hosting all three remaining presidential candidates ahead of Wisconsin’s primary next week.

Mr. Trump leads the race for the nomination, but analysts say it’s questionable whether he’ll be able to collect the delegates needed to win on a first ballot at the July convention in Cleveland.

Mr. Kasich is mathematically eliminated from any chance of winning before the convention, while Mr. Cruz would have to win 85 percent of all available remaining delegates.

Mr. Cruz said he believes that’s possible, but also said if they go to a convention, Mr. Kasich cannot be chosen because he hasn’t met the threshold of winning at least eight states — one of the requirements in the current rules.

Mr. Kasich, though, said he expects the convention to turn to him as the candidate most likely to win against Democrats in November.

“The convention is nothing more than an extension of the process we have going on now,” Mr. Kasich said.

For his part, Mr. Trump seemed to stumble Tuesday when he said education and health care are two of the top three functions of the federal government, along with national security.

That stance is at odds with many conservatives who say neither of those appears in the Constitution and both should be left to the states to handle.

Pressed by Mr. Cooper, Mr. Trump tried to clarify, saying both health care and education are part of “the concept of the country,” and the federal government should lead in those areas. But he said he wants private companies to be the major force in health and would end the Common Core education standards the Obama administration has pressed on the states.

Mr. Trump also defended his campaign manager, Corey Lewandowski, who was charged with simple battery Tuesday after an encounter with reporter Michelle Fields, who at the time worked for Breitbart News. A newly released security video showed Mr. Lewandowski accosting Ms. Fields as she tried to get Mr. Trump’s attention after a press conference in Florida, touching the candidate.

“She shouldn’t have been touching me,” Mr. Trump said.

Mr. Lewandowski initially had said he never touched the reporter. Mr. Trump did not explain the discrepancy Tuesday, but instead said Ms. Fields’ own version had changed — she initially said she was almost dragged down, while the video does not seem to show that.

Mr. Trump said he will not fire Mr. Lewandowski, and said the video exonerates him.

“I stick up for people when people are unjustly accused,” he said.

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