Megyn Kelly: I'm not apologizing to Trump for 'doing good journalism'
Fox News host Megyn Kelly on Aug. 10, 2015. (Screenshot/YouTube)

Fox News host Megyn Kelly did not directly address the personal attacks against her by Donald Trump on Monday, but did not back down from pressing the Republican presidential candidate over his history of sexist remarks.

"Trump, the front-runner, will not apologize. And I certainly will not apologize for doing good journalism," she said. "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."

The former reality TV star accused Kelly of having "blood coming out of her wherever" for bringing the issue up at last week's candidate debate.

He was subsequently disinvited from an event hosted by the conservative site, and later demanded an apology from Kelly. Kelly noted the attacks during a short commentary on her show, saying she declined to respond.

"I felt he was asked a tough but fair question. We agreed to disagree," she said, later adding, "This is a tough business, and it's time now to move forward."

CNN reported that Trump and the network's CEO, had what was described as a "blunt but cordial" conversation on Monday morning.

"We discussed our concerns, and I again expressed my confidence in Megyn Kelly," Ailes said in a statement. "She is a brilliant journalist and I support her 100 percent."

Watch Kelly's commentary, as aired on Monday, below.