NEW YORK - US talk show star David Letterman apologized on the air to his wife who he said had been "horribly hurt" by his admission that he had sexual affairs with staffers.

Letterman also offered a mea culpa to his staff in the show aired late Monday. He said they had been "wonderfully supportive" since the furore over his trysts and a two million dollar blackmail attempt erupted.

The 62-year-old comic made his apology in the first show taped since his admission Thursday that he had sex with coworkers and had been the target of an extortion attempt.

Letterman said he will need to work hard to patch up the relationship with his wife, Regina Lasko, who he married in March, 16 years after they started dating. The couple have a son.

"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," Letterman told the studio audience.

"Let me tell you folks, I've got my work cut out for me."

Letterman has become a central target for US newspapers, cable news and entertainment media. But he tried to maintain his humour in the latest appearance.

"I mean, I'll be honest with you folks," he said. "Right now, I would give anything to be hiking on the Appalachian Trail. I got in the car this morning, and the navigation lady wasn't speaking to me."

Letterman dropped his bombshell on Thursday night's show, telling a stunned audience: "I have had sex with women who work on this show."

He then provided details about an extortion scheme in which a man tried to blackmail him three weeks ago by threatening to go public about the liaisons.

Letterman reported the matter to his lawyer and the Manhattan District Attorney's office, leading to the arrest of CBS producer Robert Halderman.

Halderman, 51, has pleaded not guilty to charges of first degree attempted grand larceny and reportedly has been suspended from his job.

On Monday Letterman apologized for putting his staff in an uncomfortable position with the revelations.

"It was very, very unpleasant, and I'd just like to set the record straight: No, I'm not having sex with these women. Those episodes are in the past," Letterman said.

The revelation led to a surge of on-air expostulating on cable television about his behavior with staff, the occasionally flippant tone he used on Thursday, and the potential ratings boon he could make from the affair.

But the comic, who just last month hosted President Barack Obama on his show, insisted Monday that he handled the incident appropriately.

"Through all of the heartache and the attention and the embarrassment, I still feel like I did the right thing," he said.