NEW YORK (CNN) -- Late-night talk show host David Letterman offered a "heartfelt" apology before a live studio audience Monday to his wife and female staffers over last week's "sextortion" revelations, fans at the taping said.
David Letterman has mined private events in his life for very public jokes on his show.
"He really handled it head on, but it was funny too," audience member Larry Lefkowitz of Brooklyn Heights, New York, told CNN after the taping.
"You could tell he'd been though a difficult situation and that he was sorry that he hurt other people, but he was also able to keep it funny, throw humor into it too," Lefkowitz said.
Letterman revealed on his show Thursday night he had sex with members of his staff and that he testified about those liaisons before a New York grand jury for a case involving an alleged attempted extortion.
A CBS producer is accused of threatening to go public with allegedly embarrassing information about Letterman's private life, unless the 62-year-old funnyman paid $2 million.
Monday's mea culpa marked his first public remarks since last week's admission.
"The staff here has been wonderfully supportive to me, not just through this furor, but through all the years that we've been on television. ... So, again, my thanks to the staff for, once again, putting up with something stupid I've gotten myself involved in," Letterman said, according to excerpts released Monday by production company World Wide Pants.
"Now the other thing is my wife, Regina. She has been horribly hurt by my behavior, and when something happens like that, if you hurt a person and it's your responsibility, you try to fix it. And at that point, there's only two things that can happen: Either you're going to make some progress and get it fixed, or you're going to fall short and perhaps not get it fixed, so let me tell you folks, I got my work cut out for me."
Another audience member said Letterman's apology to his wife appeared to evoke sympathy from some in the crowd.
"When he made the apology to his wife he was very serious, not looking for any laughs, when he said he had a lot of work -- a lot of work to do on the homefront," said a man who identified himself as John.
"That was very heartfelt, a lot of women in the crowd -- I could hear them literally saying, 'awww,' that they felt for Dave and the dilemma he's probably going through."
Although Letterman first admitted the plot and sexual relationships very publicly on his show, most videos of the segment were taken down from YouTube this weekend at the request of CBS.
The New York Times reported an unnamed source said CBS made the copyright infringement claim at the request of Worldwide Pants Inc., the production company owned by Letterman which produces his show.
CBS and Google, which owns YouTube, both had no comment about the videos being taken down.
At least some fans appear willing to forgive Letterman for his admitted dalliances.
"I still think he's the king of late night comedy," Lefkowitz said.
CNN's Doug Ganley contributed to this report