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 previous year for his reporting on allegations against the disgraced Hollywood producer Harvey Weinstein.
"Some of you may be aware of what's been going on in my life for the past few days", she said at the opening of the show.
"If you (CBS) were to take action today and you are wrong, you open yourself up to potential liability", said Charles Elson, director of the Weinberg Center for Corporate Governance at the University of Delaware.
CBS said on Monday it would postpone its 2018 annual shareholder meeting that was previously scheduled for August 10 to an unspecified date.
Kirgo - one of the six women whose experience with Moonves was included in the magazine story - said the meeting "went really well" but was surprised when Moonves, who was married to Nancy Wiesenfeld at the time, asked to meet her privately over dinner.
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Firefighters tried in vain to build containment around the blaze Thursday, but flames kept jumping their lines, he said. A city in California has been left looking like hell on earth after a rapidly moving wildfire jumped across a river.
That was the last Kirgo heard from Moonves, she told NPR.
On Friday, she tweeted that she "fully supported" Moonves, calling him a "kind, decent and moral human being".
In another case, in 1985, the writer Janet Jones also described Moonves trying to kiss her during a business meeting at his office. CBS said that Moonves has no recollection of the interactions with Jones.
Mr Moonves, who is chairman and chief executive of CBS, told the New Yorker he regretted "immensely" having "made some women uncomfortable" in the past. "All allegations of personal misconduct are to be taken seriously", they said in a statement. The allegations come as CBS is at the center of a very public legal dispute with Shari Redstone and her National Amusements for control of the company. Moonves issued a statement apologizing for some of his past actions but reiterated that he never used his position of power to hinder anyone's career. CBS has had little time to react, and the piece is already eating into the company's stock price. Moonves, 68, joined the former CBS Corporation in 1995 as President of CBS Entertainment. They also called out a general culture among executives at CBS wherein the men protected and promoted each other while women were harassed and dismissed.