The Alaska governor appeared on NBC's "Today" show Friday, continuing a feud with the CBS "Late Show" funnyman over his joke earlier this week that Palin's daughter got "knocked up" by New York Yankee third baseman Alex Rodriguez during their recent trip to New York.
Palin also said she doesn't believe she should be automatically considered the front-runner for the Republican presidential nomination in 2012.
Asked by Matt Lauer whether Letterman owed her daughter an apology, the former vice presidential candidate broadened it.
"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."
Letterman has said his joke was about Palin's 18-year-old daughter Bristol, who is an unwed mother (no name was used). Problem was, the Alaska governor was traveling with 14-year-old Willow. Palin said it took Letterman time to think of the "convenient excuse" that he was talking about Bristol instead of Willow.
Letterman said on his show Wednesday that he would "never, ever make jokes about raping or having sex of any description with a 14-year-old girl." He said he was guilty of poor taste.
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."
She said there was a double standard where the media treats President Barack Obama's family as generally off-limits while her family was the target of jokes during last fall's presidential campaign and beyond.
Palin denied that it was also in bad taste for her spokeswoman, Meghan Stapleton, to say Thursday that Palin would not appear on Letterman's "Late Show" because "it would be wise to keep Willow away from David Letterman."
"Maybe he couldn't be trusted because Willow has had enough of this type of comments and maybe Willow would want to react to him in a way that maybe would catch him off-guard," she said. "That's one way to interpret such a comment."
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.
Asked if her run for the vice presidency last year with Sen. John McCain effectively puts her in the position of front-runner for the Republican presidential nomination in 2012, Palin replied, "Oh, heck no."
"Not necessarily me. I don't think I need any kind of title in order to effect change," she said.
Asked if she should have the right of first refusal of the party's nod, Palin said: "Nobody's entitled to that right of approval. There's no entitlement accepted, I believe, in our party. You have to walk the walk, not just talk the talk. ... Your accomplishments have to speak for themselves."