Fox News Chairman and CEO Roger Ailes called Republican presidential front-runner Donald Trump Monday morning to extend an olive branch after the billionaire real estate mogul attacked Fox host and GOP primary debate moderator Megyn Kelly over what he said was unfair questioning during the debate.

"Donald Trump and I spoke today," Ailes said in a statement released by the network Monday night, reported Politico. "We discussed our concerns, and I again expressed my confidence in Megyn Kelly. She is a brilliant journalist and I support her 100 percent. I assured him that we will continue to cover this campaign with fairness & balance. We had a blunt but cordial conversation and the air has been cleared."

Trump also sent a tweet out: "Roger Ailes just called. He is a great guy & assures me that 'Trump' will be treated fairly on @FoxNews. His word is always good!"

Trump had reportedly threatened to boycott Fox News altogether, but after speaking with Ailes, he gave a policy-centered phone interview to "Fox & Friends" Tuesday morning, steering clear of his weekend-long fight. He is also scheduled to make an hour-long appearance on "Hannity" on Monday night.

During Thursday night's prime time debate, Kelly challenged Trump over disparaging comments he had made about various women in the past, to which Trump responded that perhaps he should say something nasty about her. Following the debate, Trump took to Twitter, saying that Fox's questioning was unfair and that he was being targeted. He called Kelly a "bimbo" and said in a CNN interview that Kelly was so angry that she had "blood coming out of her eyes, blood coming out of her wherever."

That comment sparked an uproar as many believed that Trump was implying that Kelly took a tough stance because she was on her menstrual cycle. Trump refused to apologize, insisting that he simply meant Kelly was angry. He later said that she actually owed him an apology, and went on to give interviews to a number of news networks, but reportedly declined to appear on Fox.

Upon returning, Trump made only a passing reference to the spat with Kelly. Host Steve Doocy greeted him with, "Glad we're friends again."

"We are friends, Steve. We've always been friends," Trump responded, before vaguely touching on various policy positions, according to USA Today

On taxes, Trump said he would "start off by simplifying our current system. Put H&R Block out of business ... make it nice and easy for people to understand and reduce taxes."

Trump didn't directly answer when Doocy asked whether he would support sending troops into combat to fight the Islamic State group. "I was not a fan of going to Iraq," he said. But "now that we are there and you have these people chopping off Christians' heads ... I say cut them off where they are getting their wealth: Cut them off at the oil."

"We go in, we knock the hell out of them, we take the oil, we thereby take their wealth," he added.

Trump also continued to refuse to promise that he will not run as an independent if he doesn't get the Republican nomination. "We're going to keep the door open, we are going to see what happens," Trump said. "I do want to keep that door open in case I don't get treated fairly."

Kelly addressed the "dustup" for the first time during her show Monday evening, delivering a blistering rebuttal against Trump.

"Trump, who is the front-runner, will not apologize. And I certainly will not apologize for doing good journalism," Kelly said, according to The Huffington Post. "So I'll continue doing my job without fear or favor. And Mr. Trump, I expect, will continue with what has been a successful campaign thus far ... This is a tough business and it is time now to move forward."