Donald Trump said Monday he doesn’t really care if people like Ohio Gov. John Kasich endorse him — but he also didn’t contradict Republican National Committee Chairman Reince Priebus, who on Sunday hinted at possible retribution for such holdout Republicans.

“I really don’t care. That’s not up to me — that’s up to them,” Mr. Trump said on “Fox and Friends.” “They signed a very, very strong pledge, and they signed it because they wanted me to sign it.”

Mr. Trump is referring to a pledge the Republican presidential candidates took to support the party’s eventual nominee. Several of Mr. Trump’s former 2016 GOP rivals like Mr. Kasich, former Florida Gov. Jeb Bush and Sen. Ted Cruz have yet to explicitly endorse him.

“Now … there were three or four of them that didn’t honor it, and the reason they didn’t honor it is [because] they got beaten so badly,” Mr. Trump said.

“I mean, I beat Kasich so badly that it was unbelievable,” he said.

Mr. Trump said he and GOP Sen. Rob Portman, who is running for re-election in Ohio, have a “great relationship.”

“But Kasich isn’t on board, and the only reason he’s not on board is that he got beaten so badly. He got beaten as badly as anybody can get beaten,” he said.

“I don’t mind it. If Kasich doesn’t endorse me that’s fine,” he said. “But I will say this: He and Bush and all of these people signed pledges.”

On Sunday, Mr. Priebus had hinted at potentially throwing up roadblocks for people who aren’t backing Mr. Trump if and when they decide to run for office again.

“If they’re thinking they’re going to run again someday, I think that we’re going to evaluate … the nomination process, and I don’t think it’s going to be that easy for them,” Mr. Priebus said on CBS’s “Face the Nation.”

John Weaver, who had been the Kasich campaign’s chief strategist, hit back in a statement Sunday evening saying the Ohio governor was not going to be “bullied by a Kenosha political operative that is unable to stand up for core principles or beliefs.”

Mr. Trump said Monday that Mr. Priebus is doing “a very good job.”

“But it shows he’s a tough cookie. He doesn’t like it when you sign a pledge and then you use their data,” he said. “They signed an agreement … and now they’re violating it.”

“These people all want to run in four years, right? If I were the head of the Republican Party, I’d say you can’t do it, but what do I have to do with it?” Mr. Trump said. “In the meantime, we’re either tied or leading, we’re doing very well, and it’d be nice to have their support, but at this point, I don’t really even care about their support. Whatever happens happens.”