Sarah Palin has accepted comedian David Letterman’s apology made during Monday night’s broadcast of “The Late Show” for crude jokes made about her and her teen daughters last week.

In a statement to FOXNews.com early Tuesday, the Alaska governor said, "Of course it's accepted on behalf of young women, like my daughters, who hope men who 'joke' about public displays of sexual exploitation of girls will soon evolve."

"Letterman certainly has the right to 'joke' about whatever he wants to, and thankfully we have the right to express our reaction," Palin said. "This is all thanks to our U.S. Military women and men putting their lives on the line for us to secure America's Right to Free Speech - in this case, may that right be used to promote equality and respect."

The apology came after David Letterman took his biggest step to put the furor surrounding his jokes about Gov. Sarah Palin's daughters behind him.

"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," Letterman told the studio audience.

Click to read about reactions from women's advocacy groups to Letterman's joke.

He went on to explain how he had come to the realization that last week's monologue, in which he joked about one of Governor Palin's teenage daughters being "knocked up" by New York Yankee Alex Rodriguez, could be interpreted as being in poor taste.

"I thought I was telling it about the older daughter being at Yankee Stadium. And it was kind of a coarse joke. There’s no getting around it, but I never thought it was anybody other than the older daughter, and before the show, I checked to make sure in fact that she is of legal age, 18. Yeah. But the joke really, in and of itself, can’t be defended."

He said he didn't know that Palin's 14-year-old daughter was attending the game with her.

"Now people are getting angry and they're saying, 'Well, how can you say something like that about a 14-year-old girl, and does that make you feel good to make those horrible jokes about a kid who's completely innocent, minding her own business,' and, turns out, she was at the ball game," Letterman said.

"I had no idea she was there. So she's now at the ball game and people think that I made the joke about her. And, but still, I’m wondering, 'Well, what can I do to help people understand that I would never make a joke like this?' I’ve never made jokes like this as long as we've been on the air, 30 long years, and you can't really be doing jokes like that. And I understand, of course, why people are upset. I would be upset myself."

Letterman's mea culpa comes on the heels of New York State Assembly Minority Leader Brian Kolb's calls to the CEO of CBS to fire David Letterman. In the letter to CBS chief Les Moonves, Kolb said he took Letterman to task for the "shockingly inappropriate" jokes.

“As the proud father of a daughter, and as a husband, I wanted Mr. Moonves to hear from me directly about Mr. Letterman’s disparaging remarks," Kolb said in a written statement.

“Firing Mr. Letterman would send a clear message that CBS will not tolerate any of its employees — even an established media figure like Mr. Letterman — making demeaning and degrading comments about women.”

The talk show host has also been blasted by women's groups

"There's a saying that out of the heart, the mouth speaks, and Letterman's statement reveals a pretty ugly reflection of who Letterman may be," Wendy Wright, president of Concerned Women for America, told FOXNews.com.

"When he said those things, they were thought through. He probably kicked them around with his writers who thought it was appropriate to say these reprehensible things."