US TV
The chatshow host recently said that he regretted that the quips he made about the politician's 14-year-old daughter being "knocked up" by Alex Rodriquez were misconstrued, when they intended for her eldest, Bristol, 18.
Letterman issued an official apology during Monday night’s broadcast of his programme, E! reports.
He said: "It doesn't make any difference what my intent was, it's the perception... I take full blame for that. I told a bad joke. I told a joke that was beyond flawed, and my intent is completely meaningless compared to the perception."
He added: "So I would like to apologise, 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."
Last week, Palin appeared on the Today show, calling for Letterman to apologise to all young women in the US for his inappropriate jabs.
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