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

White House counselor Kellyanne ConwayKellyanne Elizabeth ConwayTrump has floated Mnuchin, Conway for White House chief of staff: report Trump embarks on Twitter spree amid impeachment inquiry, Syria outrage The Hill's Campaign Report: Biden camp faces new challenges 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 want Warren to talk costs on 'Medicare for All' Khashoggi fiancée meets with lawmakers seeking 'justice and accountability' for his slaying Schiff should consider using RICO framework to organize impeachment 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 LauerWomen's advocacy group calls on DNC to cancel MSNBC debate after rejection of new Lauer investigation Former NBC hosts call for reversal of rejection of sexual misconduct investigation NBC-Universal rejects outside investigation of Matt Lauer MORE, Charlie RoseCharles Peete RoseCBS defends decision to bring back 'Bull' after allegations against star Scott Pelley: Complaints to execs about 'hostile' workplace led to ouster from CBS Evening News Study finds misconduct is the top reason CEOs are leaving large companies 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.