The head of the Republican Party told NBC on Monday that he thinks GOP presidential candidates should vow not to run as third-party candidates if they do not win the party's nomination, something front-runner Donald Trump has said could happen should he be treated unfairly.

"I think our candidates should pledge not to run as a third-party candidate. I don't see that happening," Reince Priebus, chairman of the Republican National Committee, said Monday on NBC's "Today."

As HNGN reported, 69-year-old Trump said last week that he would consider mounting a third-party bid if the Republican Party treats him unfairly during the primary process.

"The RNC (Republican National Committee) has not been supportive," Trump said in a 40-minute interview with The Hill. "They were always supportive when I was a contributor. I was their fair-haired boy. The RNC has been, I think, very foolish."

But Priebus said that he is not worried about Trump launching his own independent bid because all 16 of the party's contenders understand the importance of uniting together to beat former Secretary of State and Democrat frontrunner Hillary Clinton.

"I don't fear that, and I think you've even seen Donald Trump walk that back over the last few days as well," he said.

"I think everyone understands that if Hillary Clinton is going to get beat, she's 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'll have to run as a Republican," Priebus told NBC.

Despite a slew of controversial comments from Trump in recent weeks regarding illegal immigrants and Sen. John McCain's status as a war hero, he still led the pack in several polls released on Sunday. The RealClearPolitics average of polls shows him in first place with 18.2 percent support, followed by former Florida Gov. Jeb Bush with 13.7 percent and Wisconsin Gov. Scott Walker with 11.7 percent.

Priebus said that Trump's surge is likely a result of him "speaking out to people that are really frustrated with Washington," noting that "there's an element of that in both parties," referring to Vermont Sen. Bernie Sanders' Democratic campaign.

Priebus also dismissed the idea that Trump could be damaging the party's image with his bold rhetoric.

"I think people understand that everyone speaks for themselves, and I'm not worried about that. But I do agree that tone matters and how you speak matters. It's kind of like what our moms all told us: Sometimes it's not what you say, it's how you say it. And I think that's very clear. I think that most people understand that," he said.