Ms. King continued: “I’ve enjoyed a friendship and a partnership with Charlie for the past five years. I have held him in such high regard. And I am really struggling. Because how do you — what do you say when someone that you deeply care about has done something that is so horrible. How do you wrap your brain around that?”

As a wave of harassment claims has cascaded across industries, news organizations have increasingly faced the delicate task of covering allegations against their own employees.

Mark Halperin of NBC News, the former New Republic literary editor Leon Wieseltier and Michael Oreskes, National Public Radio’s top editor, are among the prominent media figures to be accused of sexual misconduct. On Monday, The New York Times suspended Glenn Thrush, one of its White House correspondents, after the website Vox published an article in which four women described him engaging in inappropriate sexual behavior.

On CBS, Ms. O’Donnell praised the women who spoke to The Washington Post and other news outlets about Mr. Rose’s behavior.

“This is a moment that demands a frank and honest assessment about where we stand and more generally the safety of women,” Ms. O’Donnell said. “Let me be very clear: There is no excuse for this alleged behavior. It is systematic and pervasive. And I’ve been doing a lot of listening, and I’m going to continue to do that.

“This I know is true: Women cannot achieve equality in the workplace or in society until there is a reckoning and a taking of responsibility,” she continued. “This will be investigated. This has to end. This behavior is wrong, period.”

Ms. King and Ms. O’Donnell said that they had not yet spoken to Mr. Rose about the allegations against him, but that they planned to. On Monday, Mr. Rose issued a statement apologizing for his behavior and calling himself “greatly embarrassed,” although he said he did not believe all of the allegations were accurate.