The board of CBS Corporation spent most of the weekend discussing what immediate actions it should take involving Les Moonves, the company’s chief executive, after a published report that included allegations of sexual misconduct from six women.

At least two of the board’s 14 members have questioned whether Mr. Moonves should continue to run the company during an internal investigation, according to two people familiar with the conversations who asked not to be named because the matter was confidential. The board has also discussed how they should proceed with the investigation.

The board hopes to hammer out some of the details, including the scope of the inquiry, during a regularly scheduled meeting on Monday, the people said. CBS declined to comment on board discussions on Sunday.

The investigation was prompted by a report in The New Yorker on Friday that included detailed descriptions of allegations from six women who said that Mr. Moonves had asked them for sexual favors and retaliated when they declined. Four women spoke on the record, including the Emmy award-winning actress Illeana Douglas, who described a 1997 meeting with Mr. Moonves during which, she said, he was “violently kissing” her while holding her down.