Republican National Chairman Reince PriebusReinhold (Reince) Richard PriebusEx-Sen. Cory Gardner joins lobbying firm Democrats claim vindication, GOP cries witch hunt as McGahn finally testifies Biden's is not a leaky ship of state — not yet MORE on Sunday urged Republican candidates not to run as independents.

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He said on NBC's "Meet the Press" that "it only makes sense" that candidates "wouldn't run as a third party," adding it would be a "death wish" to both parties.

"If you're going to run for the nomination of our private organization, which is the Republican Party, that it only makes sense that you would, number one, agree that a Republican would be better than a Democrat running on the other side and that you wouldn't run as a third party," he said.

Donald Trump recently told The Hill in an exclusive interview that the chances he will launch a third party White House run will "absolutely" increase if the RNC is unfair to him during the 2016 primary season.

"I think a third party, at least a serious one, on either side of the aisle, would be a death wish to both parties. So I don't think it's unreasonable to say that candidates ought to support on our side, the Republican nominee, if it's not them, and they ought to pledge not to run as a third party," Priebus added.

On whether he has reached out to candidates, Priebus said he hasn't made phone calls to "every candidate."

Priebus said Trump was not hurting the Republican party's image, but added, "Donald Trump speaks for Donald Trump, and no, I don't think it has anything to do with the Republican Party ... None of these candidates speak for the party."

Trump has surged in the polls with his inflammatory remarks, such as referring to illegal immigrants as "rapists" and other criminals, and his attacks on other candidates.

He said he predicted having a GOP nominee "probably by the end of March, the beginning of April."

Meanwhile, Debbie Wasserman Schultz, leader of the Democratic National Committee, addressed reports that Vice President Joe Biden is exploring a presidential run.

"There would always be room for the sitting vice president if he chooses to run" Schultz said, adding that the party has kept prospective candidates informed of its activities.

She declined to comment on Sen. Bernie Sanders's (I-Vt.) popularity, saying that it was more important to compare the Democratic candidates to the Republican ones.

Wasserman Schultz said Democratic candidates "speak to the issues that are important to the American people" and compared them to the GOP frontrunner, who she said has deemed Mexicans ‘rapists.’ "

"Our candidates and our parties stand for helping people reach the middle class, making sure that if you, you know, work hard and play by the rules, that you should have an opportunity to succeed and that you can," she said.

"And the Republican field, you know, look, you know, you've got their frontrunner, who has deemed Mexicans rapists, you had a presidential candidate Mike Huckabee this week actually not rule out that he'd used federal troops to stop abortion. Jeb Bush, who's said he'd phase out Medicare," she added.

"That contrast ... between our candidates and theirs is very clear," she said. "The American people will eventually choose our nominee as president."

Wasserman Schultz did not say when Democratic primary debates would begin but said the party has committed to six debates.

"We're going to have a robust series of debates," she said. "We'll be announcing our series of debates very soon."