During the GOP presidential debate, Donald Trump put to rest speculations that he would run as a third party candidate, saying he will not run as a third party candidate "no matter what."

He said he was "totally committed to the Republican party" and restated his intentions in an interview following the debate.

"When they asked it, I did not hesitate. I decided to just say, 'Yes, I'm a Republican. I'm not going to be doing a third-party [campaign],' " he told CNN's Chris Cuomo.

"No matter what," he added when pressed.

The issue first came up during the debate when moderator Hugh Hewitt asked Trump whether he was "ready to reassure Republicans that you will run as a Republican and abide by the decision of the Republicans" amid concerns that an independent bid would sink the GOP's chances of winning the presidency.

 "I am, I really am," Trump said.

"I've gained great respect for the Republican leadership. I've gained great respect for many — I would even say all in different forms — of the people on the stage."

He said he was "honored to be the frontrunner."

"I will do everything in my power to beat Hillary Clinton," said Trump.

Last week, candidate Dr. Ben Carson indicated he too might leave the party.

Carson responded to Hewitt's question, "The statement that I made last week that I would leave the party was contingent upon whether in fact the party acts like they have in the past, with a lot of subterfuge and dishonesty, or like they are going to act now because I spoke to [Republican National Committee Chairman] Reince Priebus," Carson said.