On Tuesday, Mr. Rose’s former co-hosts, Gayle King and Norah O’Donnell, addressed the allegations in the opening minutes of “CBS This Morning.”

“I’ve enjoyed a friendship and a partnership with Charlie for the past five years,” Ms. King said. “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?”

With Mr. Rose aboard, the network had found some success in the early hours of the day for the first time. Although it still trails NBC’s “Today” and ABC’s “Good Morning America” in the Nielsen ratings, “CBS This Morning” has narrowed what was once a significant gap.

Mr. Rose had been a centerpiece of the turnaround. The network even gave him prime speaking position at a network presentation held for advertisers and members of the press in May.

Usually a lively, news-focused broadcast, the show was grim on Tuesday, with Mr. Rose absent. Ms. King faced the camera and said: “None of us ever thought that we’d be sitting at this table in particular and telling this story. But here we are.”

The opening 10 minutes were devoted to an unvarnished account of the allegations against Mr. Rose, including a snippet from a media critic, James Warren, who said the veteran broadcaster’s career was “probably toast.”