Trump: If I were GOP chair, I would not let Republicans who refuse to back me run in 2020

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Donald Trump.

Donald Trump said Monday he did not care if his former primary challengers endorse him, but expressed agreement with Reince Priebus, the Republican National Committee chair, who warned measures may be taken against Republicans who refuse to get aboard the Trump train.

"These people all want to run in four years, right?" Trump asked on Fox News. "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?"

The real-estate mogul added: "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."

During a Sunday interview on CBS' "Face the Nation," Priebus said Trump's former primary challengers might face trouble in 2020 or 2024 if they do not announce their support for Trump.

"Those people need to get on board," he said. "And if they're thinking they're going to run again someday, I think that we're going to evaluate the process - of the nomination process and I don't think it's going to be that easy for them."

Ohio Gov. John Kasich, Sen. Ted Cruz of Texas, and former Florida Gov. Jeb Bush have prominently refused to endorse Trump since he wrapped up the party's nomination in May. Priebus said the party would "look at" potential penalties for those who have not endorsed Trump that are considering a future presidential bid. Every GOP presidential hopeful signed a loyalty pledge last summer stating they would support the eventual nominee no matter who it was.

"People in our party are talking about what we're going to do about this. I mean there's a ballot access issue in South Carolina," Priebus said. "In order to be on the ballot in South Carolina, you actually have to pledge your support to the nominee, no matter who that person is. So what's the penalty for that? It's not a threat, but that's just the question that we have a process in place."

"And if a private entity puts forward a process and has agreement with the participants in that process, and those participants don't follow through with the promises that they made in that process, what - what should a private party do about that if those same people come around in four or eight years?" he continued.

Kasich's chief strategist for his presidential run, John Weaver, fired back at Priebus late Sunday, saying the Ohio Republican would not be "bullied by a Kenosha political operative,' mentioning Priebus' hometown in Wisconsin.

The Manhattan billionaire praised Priebus in his Monday interview saying he is doing "a very good job."

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

Calling out Kasich specifically, Trump said the only reason he's not backing him is because the real estate magnate beat the governor "so badly."

"But Kasich isn't on board, and the only reason he's not on board is that he got beaten so badly," Trump said. "He got beaten as badly as anybody can get beaten. I don't mind it. If Kasich doesn't endorse me that's fine. But I will say this: He and Bush and all of these people signed pledges."