“I am not interested in basically litigating something that is finished that makes my network look bad,” Mr. O’Reilly said.

As The Times has previously reported, Ms. Kelly sent an email about Mr. O’Reilly to top Fox executives that day. On Monday, she shared part of that email with her audience.

“Perhaps he didn’t realize the kind of message his criticism sends to young women across the country about how men continue to view the issue of speaking out about sexual harassment,” she wrote. “Perhaps it’s his own history of harassment of women which has, as you both knew, resulted in payouts to more than one woman, including recently, that blinded him to the folly of saying anything other than ‘I am sorry for the women of this company who never should have gone through that.’”

Ms. Kelly, who worked at Fox News from 2004 until January of this year, also criticized Irena Briganti, the network’s top communications executive, for “vindictiveness.”

Ms. Briganti did not immediately respond to a request for comment. A spokesman for 21st Century Fox, the parent company of Fox News, said, “Irena is a valued colleague and she has our full support.”

Ms. Kelly is a month into her role as host of “Megyn Kelly Today.” The show’s ratings have gotten off to a rough start: For the week of Oct. 9, she had about 2.3 million viewers, a 23 percent drop from the figure for the same time slot a year ago.

On Thursday, in an attempt to increase the show’s fun factor, Ms. Kelly danced to a Pitbull song with Hoda Kotb, the co-host of the 10 a.m. hour of “Today.” The two women asked audience members to join them in an “Ellen”-style shindig, with limited success. A clip of the brief dance party went viral on social media.