After a public war of words, David Letterman is apologizing to the Palin family for a joke he told last week.

On last Monday's "Late Show," Letterman made a joke about Alaska governor and former Vice Presidential candidate Sarah Palin and her daughter attending a New York Yankees game, saying: "During the seventh inning, her daughter was knocked up by Alex Rodriguez."

David explains on tonight's show that he meant to joke about Palin's daughter Bristol, 18, who recently had a baby and graduated high school, but he later learned that it was Palin's 14-year-old daughter Willow who was at the Yankees game. Regardless, Letterman says, "I told a bad joke. I told a joke that was beyond flawed, and my intent is completely meaningless compared to the perception. 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 that it was misunderstood."

"So I would like to apologize," Letterman continues,"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."