The late-night host, building on Thursday's startling confessional in a potential seminal moment in his storied career, vowed to repair his relationship with his wife, Regina Lasko, whom he married in March after a years-long courtship.
"Let me tell you folks, I got my work cut out for me," he said, according to an early transcript of the program released by CBS.
Monday's show was the first Letterman had taped since Thursday, when he disclosed that he had had sexual relationships with women who worked for him and said that he had been the victim of a $2 million blackmail threat. During the hour, he also apologized to his staff.
"Inadvertently, I just wasn't thinking ahead," Letterman said. "My thanks to the staff for, once again, putting up with something stupid I've gotten myself involved in."
Letterman, 62, began dating Lasko in 1986, and they have a son, Harry, who was born in November 2003. All the affairs took place before Letterman's marriage, said Tom Keaney, spokesman for Letterman's production company, Worldwide Pants.
Letterman arrived on stage Monday to applause and cheers from his studio audience. After drinking it in, he grinned sheepishly and inquired, with a mock stammer, "Did your, did your weekend just fly by?"
After pausing for the audience's sympathetic laughter, he went on: "I mean, I'll be honest with you folks _ right now, I would give anything to be hiking on the Appalachian Trail."
"I got into the car this morning," he added, "and the navigation lady wasn't speaking to me. Ouch."
In a more somber display, Letterman voiced his mea culpas. Regarding his wife, he said that, "if you hurt a person and it's your responsibility, you try to fix it."
As Letterman faced Monday's show, and the shows that will come after, it was clear that how he deals with his messy situation could prove to be a defining chapter in his long TV career. And, with any luck, it could clinch his recent ratings victory in late-night TV.
While Letterman has joked about his affairs with female staffers, it's unclear how many women he had sex with, and he has offered no specifics.
But the CBS producer accused of blackmailing Letterman used pages from a former assistant's diary that described an affair with the "Late Show" host, a law enforcement official said Monday. The ex-assistant, Stephanie Birkitt, went to live with CBS News producer Robert Halderman, who found her diary describing her relationship with Letterman and used it to help blackmail him, the law enforcement official said Monday on the condition of anonymity because the investigation was ongoing.
Halderman, a producer for the true-crime show "48 Hours Mystery," pleaded not guilty last week to extortion charges.
The flood of attention on Letterman was inevitable, and the way he initially dealt with this maelstrom recalled an embarrassing dilemma for another star in 1995.
For a celebrity the caliber of Hugh Grant, publicity _ including speculation of career suicide _ was unavoidable when he was arrested with a prostitute on Hollywood's Sunset Strip 14 years ago. But then he retreated to NBC's "The Tonight Show" to try to explain.
Host Jay Leno wasted no time before asking an instant classic of a question: "What the hell were you thinking?!"
Grant's appearance provided him with some needed image rehab. It also vaulted ratings runner-up "Tonight" past Letterman's "Late Show," a leadership position Leno held through his retirement from late night earlier this year.
Since then, Letterman has reclaimed a ratings edge over new "Tonight" host Conan O'Brien.
And now he may have truly sealed the deal. With his masterful monologue last Thursdy, Letterman single-handedly gave a TV performance to equal the Jay-and-Hugh moment. Implicit in everything he said about his own behavior was the unspoken question: "What the hell was I thinking?"
It could be that Letterman's carefully calibrated act of self-disclosure has put him in the best spot possible to weather the situation _ and even to milk it. Beloved by viewers and critics for decades, he has abruptly freshened the enduring Letterman brand and demonstrated he still has the ability to surprise even fans who thought they knew him well.
Indeed, a legendary late-night host has nothing but praise for Letterman's skill at crisis management.
"To me, it seems Dave Letterman's handling of this is impeccable," Dick Cavett said in an e-mail. "Brave, direct, and _ dare I say it? _ manly. He has set a real example here of exactly how to behave when assaulted in such a sleazy operation."
It isn't the first time Letterman has shown finesse in managing a firestorm.
In June, he had a run-in with former Alaska Gov. Sarah Palin over jokes made at the expense of her teenage daughter. He emerged from a tumultuous few days of protests and demands for his dismissal with a ratings jolt. And thanks to the dumb-luck timing of the flap, he also handily upstaged his much-hyped NBC rival just as O'Brien was taking over as "Tonight" host.
Letterman apologized to Palin and her family in what became another one of his memorable performances. But he has never stopped making jokes at Palin's expense.
Associated Press writer Jake Coyle contributed to this report.