There had been reports Monday Donald Trump was talking with Fox about an appearance on the morning show.
Trump also tweeted Monday: "[Fox News Channel chairman] Roger Ailes just called. He is a great guy & assures me that 'Trump' will be treated fairly on @FoxNews. His word is always good!"
In a statement, Ailes said he had spoken with Trump, and Ailes spoke up for Kelly. "Donald Trump and I spoke today. We discussed our concerns, and I again expressed my confidence in Megyn Kelly," said Ailes. "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 told Fox & Friends co-host Steve Doocy ABC had run a "totally false" story that he was rethinking his statement at the debate that he would not rule out a third party candidacy. But he pointed out that he was still leading in the polls and wanted to run as a Republican.
ABC had cited a senior Trump advisor in reporting the candidate might "soon" promise not to run as a third-party candidate. But ABC backed off that a bit in an update, saying Trump had told them he has no "imminent plan" to do so, though it is at least possible he could change that.
Kelly addressed the Trump dust-up on-air Monday night.
Fresh from a weekend at the beach, she jokingly asked if anything happened in the news while she was gone, then added a few words of her own.
"Apparently, Mr. Trump thought the question I asked was unfair and felt I was attacking him," she said. "I felt he was asked a tough but fair question. We agreed to disagree. Mr. Trump did interviews over the week that attacked me personally. I've decided not to respond. Mr. Trump is an interesting man who has captured the attention of the electorate. That's why he is leading in the polls. Trump who is the front-runner will not apologize and I certainly will not apologize for doing good journalism. 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."