Donald Trump’s latest round of threats for an independent bid for the White House will not scare the GOP, Republican National Committee Chairman Reince Priebus told Fox News on Tuesday.

Priebus also pushed back on claims the audience at Saturday’s South Carolina debate was unfairly stacked with big money donors who booed the billionaire businessman.

“The issue with the pledge is simply that if you are going to run as a Republican and avail yourself of the process, come to the convention, you ought to be able to say 'I’m going to support the Republican Party,'” Priebus said during an appearance on “On the Record with Greta Van Susteren.” “That’s pretty fair. I think it’s pretty standard and I am not worried about this whatsoever.”

Last summer, Trump flirted with the possibility of an independent run, but in September signed a “loyalty pledge” that committed him to the Republican Party’s nominating process. The GOP front-runner said he would honor the agreement as long as Republicans treated him fairly -- something he now claims isn’t happening.

“The RNC better get its act together,” Trump said at a campaign stop in South Carolina. “I signed a pledge. But the pledge isn’t being honored by them.”

On Monday, Trump also threatened to sue his closest rival in the race -- Texas Sen. Ted Cruz -- about his Canadian birth if Cruz does not retract alleged “lies” about Trump’s policy positions. He demanded the RNC intervene, and said if they didn’t, they’d be violating the pledge he signed in September.

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During Priebus’ appearance on Fox News on Tuesday, he also pushed back on accusations Trump made about the RNC stacking the South Carolina debate with big money donors for candidate Jeb Bush.

“Here’s the reality: When you have 600 people that are in the room that are there as guests of the candidates, guess what? They are going to be pretty excited to either be for their candidate or against other candidates,” Priebus said. “That’s pretty natural, that’s what happens, that’s what this is and I think it’s pretty normal and it’s going to continue.”

The RNC also issued a detailed memo Tuesday challenging Trump’s accusations. The memo said it is “incorrect” that they are “stacking” the debate audiences. It said that of the 1,600 tickets in South Carolina, 642 went to campaigns and only 10 went to RNC donors.