Rose was a co-host on the morning show "CBS This Morning" and a correspondent for its long-running Sunday night news magazine "60 Minutes".
Colbert said he was doing his job while King is doing her job, and she agreed.
"That's what you have to do", King, who was already scheduled to appear on the show before the allegations came down, replied. "To be honest with you, it isn't easy".
After he was sacked, CBS News said three more women who worked with Rose at CBS also accused him of sexual misconduct.
"I proceeded to go into the living room, and he said I want to show you this scene from this movie and he said have a seat, you know, relax, and he proceeded to turn on the film Secretary, which is a sexually involved film involving S&M, unfortunately", Gordon told NBC News. "Charlie and I have worked together, been friends, but when you think about the anguish of those women, despite the friendship, you still have to report the news".
Charlie Rose, one of America's most respected broadcasters, an award-winning television host and interviewer, was suspended on Monday after eight women accused him of years of sexual harassment and unwanted advances.
Rose, now 75, the latest senior male journalist accused of misconduct in the wake of the downfall of Hollywood mogul Harvey Weinstein, which opened the floodgates of sexual assault and harassment accusations in many industries.
"I'm still trying to process all of this", King said. There's certainly some anger, there's sadness, there's compassion, there's concern. There's some sadness. There's compassion.
"It feels branded into me, the details of it", Godfrey-Ryan told the paper.
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On Tuesday, Mr Trump also assailed Mr Moore's Democratic rival Doug Jones , who is now ahead in opinion polls by 47% to 42%. But he ill-advisedly shifted to the claim that "you don't need somebody who's soft on crime like Jones".
CBS News Fires Charlie Rose After Sexual Misconduct Allegations
CBS, on which Rose has co-anchored CBS This Morning since 2012, has suspended the journalist pending an investigation. In a statement to The Post , Vega said she should have done more to protect the young women on the show .
"That's what you have to do", she said.
A former intern for Charlie Rose said that Rose put her in a very uncomfortable position.
A woman who was one of Rose's assistants during the mid-2000s, Kyle Godfrey-Ryan, told The Post that Rose allegedly walked naked in front of her at least a dozen times while she was working in one of his homes in New York City.
CBS has yet to reveal Rose's replacement for its morning show. "And then it was Charlie, and I was like, 'Oh, he's a friend, I don't like that, that's hard, ' and then I thought about what these women are going through and I don't like that either".
"Women feel empowered to come up". That's what they (said), 'Just do it.
The next step, King said, is for men to join the conversation and for women to be placed in positions of power.
She added that Colbert's monologue had made her wince.
"We now have to realize that it's all bad. It's still very hurtful", she said, a day after the initial revelations.