Six women said Moonves sexually harassed them between the 1980s and late 2000s, according to a report in the New Yorker by Ronan Farrow, who earned a Pulitzer Prize past year for his reporting on allegations against the disgraced Hollywood producer Harvey Weinstein.
Directors are considering appointing a special committee to oversee its investigation, which will cover not only the specific allegations but also overall company culture.
CBS said Monday it would appoint an independent investigator to look into sexual misconduct allegations against network CEO Les Moonves, but added it had made a decision to take no further action at a board meeting. When that investigation is finished, the board will "take appropriate action", it said. Moonves could also decide to step aside voluntarily during the investigation.
Moonves was accused of sexual misconduct by six women on Friday in a report by Ronan Farrow in the New Yorker. Four women said Moonves touched them inappropriately, and two women, including the actor Illeana Douglas, said he physically intimidated them and threatened their careers.
In a statement to The New Yorker, Moonves acknowledged that he "may have made some women uncomfortable by making advances".
Also hovering is a battle over the fate of CBS that pits Moonves against Shari Redstone, who via her National Amusements umbrella company owns the majority of shares in both CBS and Viacom, its one-time corporate sibling.
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Al Jazeera's Alan Fisher, reporting from the White House , said Trump's comments at the news conference were came as a "surprise". I don't know if they're ready yet. "Good for the country, good for them, good for us and good for the world".
Moonves has been very well compensated for his company's success. "Those were mistakes, and I regret them immensely", he said.
Moonves said in a statement that he has always abided by the principle that "no means no" and he denies ever misusing his position to harm anyone's career.
The board also chose to postpone for the second time CBS' annual shareholders meeting, which had been set for August 10 in Pasadena.
"While the emotional reaction is to sell CBS on the release of the long-rumored and damaging New Yorker article regarding CBS CEO Les Moonves, we believe the stock is undervalued", Gould noted.
CBS shares were down more than 4% in early trading, dropping to the $52 range.