"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," he said during his opening monologue. "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."
Letterman also noted what a tough time this has been for both current and past staff members of his production company, Worldwide Pants.
"I'm terribly sorry that I put the staff in that position. Inadvertently, I just wasn't thinking ahead," he said. "And, moreover, 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 and especially all the years here at CBS, so, again, my thanks to the staff for, once again, putting up with something stupid I've gotten myself involved in."
But Letterman also found time for some dry humor.
The first thing he said when he walked onstage was, "Did your weekend fly by?" Letterman then started to laugh along with the crowd, according to audience members.
"He made a joke about loving the fall weather in New York, and about how it was getting mighty chilly," said an audience member from Austin. "He was making fun of the situation. If it's chilly here, you can only imagine how chilly things were at home."
Guests Steve Martin and Martin Short both poked fun at Letterman, but also acknowledged the situation was no laughing matter.
At one point Short fell backwards into Martin's lap, playing a puppet to Martin's ventriloquist. Martin joked about the other comedian getting too close and risking "sexual harassment charges."
"Dave was laughing, joking, very energetic," said an audience member. "He played off the audience's reactions, off everyone's facial expressions. But every once in a while you could tell his mind was somewhere else."
During his second taping of the day, Letterman said, "Good evening ladies and gentlemen. Welcome to the late show. Are you sure you want to be seen with me?"