Republican National Committee Chairman Reince PriebusReinhold (Reince) Richard PriebusBiden's is not a leaky ship of state — not yet Governor races to test COVID-19 response, Trump influence Ex-Trump chief of staff Priebus mulling Wisconsin governor bid MORE on Monday said GOP presidential candidates shouldn’t seek a third-party challenge for the White House, less than a week after Donald TrumpDonald TrumpVirginia GOP gubernatorial nominee acknowledges Biden was 'legitimately' elected Biden meets with DACA recipients on immigration reform Overnight Health Care: States begin lifting mask mandates after new CDC guidance | Walmart, Trader Joe's will no longer require customers to wear masks | CDC finds Pfizer, Moderna vaccines 94 percent effective in health workers MORE floated the idea in an exclusive interview with The Hill.

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“Our candidates should pledge not to run as a third-party candidate,” Priebus said on NBC’s “Today,” adding that he doesn’t expect any 2016 GOP candidate to run a third-party campaign if they don’t win the Republican nomination.

“I think everyone understands that if Hillary ClintonHillary Diane Rodham ClintonDemocrats say it's up to GOP to stop Trump 2024 Hillary Clinton to speak at Asian Americans and Pacific Islanders summit More than half of eligible Latinos voted in 2020, setting record MORE is going to get beat, she is going to get beat by a Republican and most people that run for president run to win. If our candidates want to win, then they will have to run as a Republican.”

The chairman’s comments come days after Trump told The Hill that he would “absolutely” consider a third-party bid for president if the RNC treats him unfairly through the debate process.

“The RNC has not been supportive. They were always supportive when I was a contributor. I was their fair-haired boy,” Trump said last Wednesday. “The RNC has been, I think, very foolish.”

On Sunday, Trump said RNC officials became “really nice” after The Hill interview.

“They’ve been really nice over the last few days, they’re starting to see what’s happening,” Trump said on CNN’s “State of the Union with Jake Tapper.”

The real-estate magnate turned GOP candidate has repeatedly clashed with the RNC during his brief candidacy. Priebus reportedly called Trump and asked him to tone his rhetoric down after controversial statements about Mexican immigrants. And the party issued a statement panning Trump’s recent comments on Sen. John McCain’s (R-Ariz.) war record.

Priebus didn’t directly address those criticisms of Trump but did tell “Today” host Savannah Guthrie that “tone matters and how you speak matters,” a message likely directed at Trump.

While many in the party are skeptical that he’ll finish with the nomination, Trump has been skyrocketing up the polls since last month’s announcement and is now in the top tier nationally and in early primary states.

Priebus also framed the party’s new debate format, which limits the prime-time debate to only the top 10 candidates, as the party taking control of the process. Many Republicans have criticized the party for ceding too much control to the media.

“We’ve taken control of the debates, we’ll have fewer debates, we’ll have some say over who the moderators are … and we’ll have a definite calendar,” he said. Priebus added that every candidate will debate on primary night, since the networks added a second event with the rest of the field ahead of the main-stage debate.

He added that the robust number of perspectives is good for the party and would give it a leg up over Clinton, the presumptive Democratic nominee.

“It’s not bad to have a battle instead of a coronation like Hillary Clinton,” he said.

“No one is asking the question of when is Hillary Clinton going to debate Bernie Sanders ... there seems to be no interest on the other side."