Conway to CNN's Cuomo in heated debate: 'I'll walk away' if you continue to interrupt me

White House counselor Kellyanne ConwayKellyanne Elizabeth ConwayLincoln Project ad dubs Jared Kushner the 'Secretary of Failure' Watchdog group accuses Stephen Miller of violating Hatch Act with Biden comments Hillicon Valley: Trump raises idea of delaying election, faces swift bipartisan pushback | Amazon, Apple, Facebook, Google release earnings reports | Senators ask Justice Department to investigate TikTok, Zoom MORE threatened to walk off of an interview with CNN's Chris Cuomo on Thursday night during a heated discussion over Supreme Court nominee Brett Kavanaugh.

Conway told the CNN host “don't interrupt” before saying that if Cuomo talked over her she would "walk away."

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The back-and-forth came during a segment discussing Kavanaugh's confirmation process following allegations made against him by California professor Christine Blasey Ford of sexual misconduct.

“You just told your audience you wanted to lay out everything you learned,” Conway said after Cuomo introduced the segment with a monologue updating the latest developments. “You’ve omitted cleverly a very important fact, which is Judge Kavanaugh said he wasn’t there.”

Cuomo shot back asking, “What is the difference?”

“What do you mean, 'What’s the difference?' ” Conway asked the host before Cuomo asked the question again.

Conway pushed back by mentioning the timeline of Ford's public accusation.

"Judge Kavanaugh found out the identity of the individual on Sunday for the first time. By Monday he had already given his statement to the committee. You want to lay the blame at somebody’s feet, look no further than your democratic friends starting with Sen. Feinstein," Conway said, referring to Senate Judiciary Committee ranking member Dianne FeinsteinDianne Emiel FeinsteinSenate Democrats demand answers on migrant child trafficking during pandemic Yates spars with GOP at testy hearing Democrats want Biden to debate Trump despite risks MORE (D-Calif.), before Cuomo interrupted.

"What does that have to do with it?" Cuomo asked.

"No, no, don’t interrupt," Conway replied.

"That’s just politics," Cuomo said of Feinstein's handling of a letter that Ford penned to the senator.

"You think you can talk over me, I’ll walk away. You guys begged me to come on and then you want to interrupt me. Hold on," Conway retorted.

Later in the interview, Conway asked Cuomo if he would have on women who have accused men in the media industry of sexual harassment or misconduct.

"Two individuals, two families here have been hurt," Conway said of Kavanaugh and Ford. "Your role as a dad should kick in once in a while, not your role as an anchor trying to get ratings."

"Kellyanne, I will never understand why you think coming at me personally is going to change how I am," Cuomo responded.

"I’m not coming at you personally," Conway said.

"I appreciate you judging me as a parent, as a member of the media, when we’re all bad people," Cuomo mocked.

"I didn’t say that. No, no, no, don’t put that in my mouth. I said as everyone preens around about these allegations, don’t forget the industry that’s been hit the hardest," Conway said, referring to media figures who have resigned or been fired recently, including Roger Ailes, Bill O'Reilly, Les Moonves, Jeff Fager, Matt LauerMatthew (Matt) Todd LauerComcast shareholders reject proposals for outside sexual harassment investigation at NBC Ronan Farrow fires back at Matt Lauer 'shoddy journalism' accusation: 'Just wrong' Megyn Kelly calls independent Tara Reade interview the 'wave of the future' MORE, Charlie RoseCharles Peete RoseIranian official maintains Tehran has 'no knowledge' of American hostage's whereabouts 'Bombshell' bombing at box office isn't exactly a shock — here's why '60 Minutes' producer alleges CBS News retaliated after she reported inappropriate behavior MORE, Mark Halperin and Tavis Smiley, among others, all in the face of sexual misconduct allegations.

"I don’t know how that’s relevant in any way. I really don’t. But I have to let you go," Cuomo said in trying to end the segment.

"I hope you’ll have all those women on sometimes who have made credible allegations against people in the media. Many of those men are not even any longer in the media," Conway said.

"And I’m glad you see that as a good way to reflect on what should be done in this situation here now,' Cuomo replied.

Ford says that at a party in the 1980s, Kavanaugh pinned her down on a bed and covered her mouth and attempted to take her clothes off.

Kavanaugh has staunchly denied the claim while also saying he wasn’t at the party in question.

Ford's lawyer said Thursday she is willing to testify in front of the Senate Judiciary Committee next Thursday.

The panel has scheduled a Monday hearing where they had asked to hear from both Kavanaugh and his accuser.