VIDEO: David Letterman Publically Apologizes To Wife Following Sex Scandal

Oct. 6 2009, Published 10:33 a.m. ET

A contrite David Letterman made a public apology to his wife Regina on his late-night talk show Monday night following the sex scandal that continues to dog him.

After apologizing to his staff for all the unwanted media attention, Letterman said: "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."

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VIDEO: Craig Ferguson’s Addresses “Boss” Letterman’s Sex Scandal

Earlier, Letterman apologized to his staff for the attention focused on them following his revelation last Thursday that he was being targeted in a $2 million blackmail plot for having sex with female staffers.

EXCLUSIVE: Letterman Apologizes To His Wife While Taping Show

Said Letterman: "I'm terribly sorry that I put the staff in that position. Inadvertently, I just wasn't thinking ahead. 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."