"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," the statement read.
"Letterman certainly has the right to 'joke' about whatever he wants to, and thankfully we have the right to express our reaction. And 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."
Letterman offered his second apology on air Monday night, a week after he told the controversial joke that he said was "misunderstood."
"The joke, really, in and of itself, can't be defended," Letterman said during Monday's "Late Show with David Letterman."
"I feel that I need to do the right thing here and apologize for having told that joke," Letterman said. "It's not your fault that it was misunderstood. It's my fault that it was misunderstood."
He apologized to Palin's oldest daughter, Bristol, at whom he said the joke was directed. Letterman went on to apologize, "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.
"I told a joke that was beyond flawed, and my intent is completely meaningless compared to the perception," he said, and claimed full responsibility for his comments.
Two weeks ago, on his program, Letterman joked about the governor's recent trip to New York: "One awkward moment for Sarah Palin at the Yankee game, during the seventh inning, her daughter was knocked up by Alex Rodriguez."
The joke seemed directed at Palin's 18-year-old daughter Bristol, who is an unwed mother. However, it was Palin's 14-year-old daughter, Willow, who accompanied the governor to New York.
Letterman later explained he had confused the two daughters and had Bristol in mind when he made the joke, but Palin interpreted it as directed at Willow.
Palin called the remarks a "very convenient excuse" that took him a couple of days to present.
"It was a degrading comment about a young woman. I would hope that people really start rising up and deciding it's not acceptable. No wonder young girls especially have such low self-esteem in America when we think it's funny for a so-called comedian to get away with being able to make such a remark as he did and to think that that's acceptable."
Last Wednesday, after two days of back and forth between Alaska's first family and the late-night talk show host, the Palins refused Letterman's invitation to come on his show.
Palin spoke out against Letterman's comments on NBC's "Today" show, and called upon the public to rise up in opposition. Palin supporters have called for Letterman's firing, even starting a website, www.firedavidletterman.com.