New York State Assembly Minority Leader Brian Kolb, a Republican, is calling on the CEO of CBS to fire David Letterman for crude comments he made about Sarah Palin and her daughter.

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 request came after the late-night host stopped short of apologizing for "jokes" he had made about Palin, the former Republican vice presidential nominee, and her family, including one that referred to her daughter being "knocked up" by New York Yankees baseball star Alex Rodriguez.

"We were, as we often do, making jokes about people in the news, and we made some jokes about Sarah Palin and her daughter, the 18-year-old girl, who is — her name is Bristol, that’s right, and so, then, now they’re upset with me," Letterman said.

"These are not jokes made about her 14-year-old daughter. I would never, never make jokes about raping or having sex of any description with a 14-year-old girl. I mean, look at my record. It has never happened. I don’t think it’s funny. I would never think it was funny. I wouldn’t put it in a joke."

The host later invited Palin and her husband to appear on “The Late Show,” a request they vehemently rejected.

"The Palins have no intention of providing a rating's boost for David Letterman by appearing on his show," the Alaska governor's office said in a written statement Thursday. "Plus, it would be wise to keep Willow away from David Letterman."

On Friday, the Alaska governor said Letterman owes an apology to young women across the country for the joke.

"I would like to see him apologize to young women across the country for contributing to kind of that thread that is throughout our culture that makes it sound like it is OK to talk about young girls in that way — where it's kind of OK, accepted and funny to talk about statutory rape," she said. "It's not cool. It's not funny."

Palin said Friday that it was time for people to rise up against Letterman's form of humor.

"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 such a remark as he did," she said. "I don't think that's acceptable."

“The Late Show” declined comment on Friday evening.

But the controversy may wind up giving both Palin and Letterman attention at a time both could use it. Palin is considered a potential future candidate for national office, and standing up for her family could make her a hero to her fans. Letterman is in the second week of his new competition with NBC's Conan O'Brien, and the two are running neck-and-neck in the ratings.

On his show Thursday, Letterman joked that Palin had called to invite him on a hunting trip — the punch line no doubt a reference to former Vice President Dick Cheney accidentally shooting a friend while hunting.

His other references to the controversy were more oblique. When guest Denzel Washington said he would get in trouble with Obama for making a joke about the president's big ears, Letterman clearly had something else on his mind.

"You aren't in the kind of trouble I'm in," he said.

FOXNews.com's Allison McGevna and the Associated Press contributed to this report.