"He's not a sexual predator," Gingrich exclaimed, cutting her off. "You can't say that. You could not defend that statement. Now, I'm sick and tired of people like you using language that's inflammatory, that's not true."
Kelly replied, pointing out that she had not taken a position on the matter herself: "Excuse me, Mr Speaker. You have no idea if it's true or not."
Gingrich was on Fox News in his role as a Trump surrogate and questioned the stories of women who've come forward to accuse Trump of sexual assault - and the relative importance of the controversy itself, relative to Democrat candidate Hillary Clinton's alleged misdeeds.
Kelly pushed back. "As a media story, we don't get to say that 10 women are lying. We have to cover that story, sir," she said.
"Sure. OK. So, so it's worth 23 minutes of the three networks to cover that story, and Hillary Clinton had a secret speech in Brazil to a bank that pays her US$225,000 [$314,265], saying her dream is an open border where 600 million people could come to America - that's not worth covering?"
"That is worth covering," Kelly interjected. "And we did."
Gingrich was still speaking: "I mean, you want to go back through the tapes of your show recently, you are fascinated with sex, and you don't care about public policy."
At that point, Kelly glanced up and past the camera, with the look of someone who wasn't quite sure she'd heard what she thought she'd heard.
"Me? Really?" she said, laughing.
"Well, that's what I get out of watching you tonight," said Gingrich.
Kelly responded, at times interrupted by Gingrich: "You know what, Mr Speaker, I'm not fascinated by sex. But I am fascinated by the protection of women and understanding what we're getting in the Oval Office and I think the American voters would like to know."
Gingrich replied: "And therefore we're going to send Bill Clinton back to the East Wing, because after all, you are worried about sexual predators."
Kelly said polls showed women and men believed the allegations were "a real issue" and told Gingrich that he shouldn't "dismiss the women summarily".
Gingrich hit back, asking: "Do you want to comment on whether the Clinton ticket has a relationship to a sexual predator."
Three women who have publicly accused Bill Clinton of sexual misconduct have criticised Hillary Clinton during the presidential campaign and come out as supporters of Trump. Bill Clinton has admitted to having extramarital affairs with two other women, Monica Lewinsky and Gennifer Flowers.
When Kelly said her show The Kelly File had covered the Bill Clinton story, Gingrich replied: "No, I just want to hear you use the words. I want to hear you use the words, 'Bill Clinton, sexual predator'. Say, 'Bill Clinton, sexual predator'."
Gingrich continued: "Disbarred by the Iowa, by the Arkansas bar ... US$850,000 penalty."
When Kelly pointed out that Bill Clinton is "not on the ticket", Gingrich fired back: He'll be in the East Wing."
While the West Wing is the area of the White House complex that generally serves as the president, the East Wing is where the president lives and serves as the office space for the president's spouse.
Kelly got in one last dig, saying, "The American public is less interested in the deeds of Hillary Clinton's husband than they are in the deeds of the man who asks us to make him president, Donald Trump," before drawing the exchange to a close with a bit of stinging advice: "You can take your anger issues and spend some time working on them, Mr Speaker."
Gingrich replied: "And you too." Dan Scavino Jr, the Trump campaign's social media director, took to Twitter to attack Kelly's performance, tweeting: "@MegynKelly made a total fool out of herself tonight- attacking @realDonaldTrump. Watch what happens to her after this election is over."
There was plenty of support for Kelly, among the tweets praising her this from @Active4Ever: "Wow, Gingrich is mansplaining and finger pointing, but Megan Kelly isn't buying it, in fact she's going right back at him! Awesome."
