US talkshow host David Letterman sought to draw a line under his feud with Sarah Palin on Monday, apologizing for making a raunchy joke about the Republican politican's 14-year-old daughter.

In a transcript of remarks Letterman was to deliver on CBS Television's "The Late Show" later Monday, the 62-year-old funnyman issued a heartfelt apology for a gag that drew a furious response from Palin, who is governor of Alaska.

Letterman's gag referred to Palin's daughter being "knocked up" by baseball star Alex Rodriguez after the governor and her family recently attended a New York Yankees game.

Letterman said although his joke had meant to target Palin's 18-year-old daughter, Bristol -- whose teenage pregnancy became a talking point during last year's presidential election campaign -- his intent was irrelevant.

"I told a joke that was beyond flawed, and my intent is completely meaningless compared to the perception," Letterman said.

"And since it was a joke I told, I feel that I need to do the right thing here and apologize for having told that joke. It's not your fault that it was misunderstood, it's my fault.

"So I would like to apologize, especially to the two daughters involved, Bristol and Willow, and also to the governor and her family and everybody else who was outraged by the joke.

"I'm sorry about it and I'll try to do better in the future."

Palin had lambasted Letterman on Friday, telling NBC's Today program that the veteran chatshow king had "crossed a line."

"It was a degrading comment about a young woman and I would hope that people start really rising up in deciding it's not acceptable," Palin said.

"No wonder young girls especially have such low self esteem in America when we think it's funny for a so-called comedian to make such a remark."

Palin had earlier decried the joke as "inappropriate" and "sexually perverted," saying it contributed "to the atrociously high rate of sexual exploitation of minors by older men who use and abuse others."