David Letterman opened The Late Show on Monday with a public apology to his wife, amid claims he kept a secret bedroom at his New York TV studio for trysts with female employees.

In a TV confession on last Thursday's show, the veteran host told viewers he was being blackmailed by an individual – now named as CBS News employee Robert Halderman - who was threatening to reveal details of his alleged flings with members of his staff.

Now he is saying sorry to his wife Regina Lasko.

After making a few jokes at his own expense, he told viewers: "She has been horribly hurt by my behaviour, and when something happens like that, if you hurt a person and it's your responsibility, you try to fix it. 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.

"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 furour, 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."

Meanwhile, staff at the Late Show claim Letterman would invite certain 'favourite' female employees to a special room dubbed 'the bunker' in the Ed Sullivan Theatre where his show is taped.