The Alaska governor, in a statement issued Tuesday, said the apology was accepted "on behalf of all young women, like my daughters, who hope men who `joke' about public displays of sexual exploitation of girls will soon evolve."
On his CBS' "Late Show" on Monday night, Letterman said his joke about one of Palin's daughters being "knocked up" by Alex Rodriguez can't be defended.
He said the joke referred to 18-year-old Bristol Palin, not her 14-year-old sister Willow. But Letterman said it's his responsibility that people believed that he intended to target Willow, who had attended a New York Yankees game with her mother.
"I'm sorry about it, and I'll try to do better in the future," he said.
Letterman last week tried to make light of the joke after the first indications that it fallen flat. Palin had called the comments "sexually perverted," and her husband, Todd, said that "any jokes about raping my 14-year-old are despicable."
Palin said Tuesday that Letterman has the right to joke about whatever he wants to, and "thankfully we have the right to express our reaction."
"This is all thanks to our U.S. military men and women putting their lives on the line for us to secure American's right to free speech," she said. "In this case, may that right be used to promote equality and respect."
Although Bristol, an unwed mother, was the target of his joke, Letterman didn't name her when it was originally made on June 8.
It was "a coarse joke," "a bad joke," Letterman told viewers. "But I never thought it was (about) anybody other than the older daughter, and before the show, I checked to make sure, in fact, that she is of legal age, 18."
"The joke, really, in and of itself, can't be defended," he declared.
If there's a misconception that he was making the joke about a 14-year-old, Letterman said he understands why people are upset. "I would be upset myself," he said.
"I feel that I need to do the right thing here and apologize for having told that joke," he said. "It's not your fault that it was misunderstood, it's my fault that it was misunderstood."
Letterman made several references to the issue during his monologue, introducing himself as "Dave Letterman, good will ambassador." He said he got a call from his mother earlier in the day telling him she was siding with Palin.
When he began a joke about Bernard Madoff, whom he called "the most hated man in America," he then amended that to a list of two.
"Me, Bernie Madoff," he said. "He was waaay out in front until a couple of days ago."