The president of a national women's public policy group on Thursday blasted David Letterman's "offensive" jokes about Sarah Palin and her daughter and called on the CBS late-night host to formally apologize.

"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."

Letterman has been under fire since he made several jokes about the Alaska governor and her daughter on his show Tuesday night, following a visit they made to New York City. In one joke, he characterized the former vice presidential candidate's style as that of a "slutty flight attendant." And in another, he joked that Palin's daughter had been "knocked up" by Yankees star Alex Rodriguez during the seventh-inning stretch of a Yankees game.

Critics jumped on Letterman soon after the show aired, accusing the comedian of making crass jokes about child rape because the girl who accompanied Palin to New York was her 14-year-old daughter, Willow, and not 18-year-old Bristol, who is the unmarried mother of Palin's first grandchild.

Letterman, on his Wednesday night show, addressed the controversy but stopped short of apologizing.

“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 on his Wednesday telecast.

“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.”

He then invited Palin and her husband, Todd, to be his guests on his show, but Palin declined. "The Palins have no intention of providing a rating's boost for David Letterman by appearing on his show," a statement to FOXNews.com read.

RELATED: Sarah Palin Declines David Letterman's On-Air Invitation.

On Thursday, Wright, whose group advocates biblical values and family traditions, called on Letterman to issue a "real" apology, saying his comments were "worse than" merely poor taste.

"The apology was inadequate and it was only about one of the statements," Wright said. "Letterman's very poor view of women and minor girls is very disturbing, and he certainly needs to do more to change his own attitudes and then prove that his attitude has changed."

She called on Letterman to contact Palin personally rather than address the issue on air. "He needs to reach out to Sarah Palin," she said. "Apparently he feels threatened by the fact that she's a beautiful conservative woman. He would've never said anything like that if Sarah Palin was a liberal. He needs to treat Sarah Palin with the respect and dignity she deserves."

The National Organization of Women also blasted Letterman for inappropriate "jokes" on its Web site Thursday.

"Comedians in search of a laugh should really know better than to snicker about men having sex with teenage girls (or young women) less than half their age," NOW said.

"The sexualization of girls and women in the media is reaching new lows these days — it is exploitative and has a negative effect on how all women and girls are perceived and how they view themselves."

FOXNews.com wasn't allowed into the taping of Thursday night's "Late Show," but audience members afterward said Letterman again addressed the controversy, joking that Palin must have forgiven him because she called him up and invited him to go hunting.

Deborah Donovan Rice, executive director of Stop It Now, an organization aiming to prevent the sexual abuse of children, also denounced Letterman's jokes and praised Palin's response as "spot on."

"This wasn't the usual fun, creative stuff I usually see on Letterman," Rice told FOXNews.com. "This really dropped below the bar."

Outside the Ed Sullivan Theater in New York Thursday afternoon, most of the studio audience lined up for the taping of Letterman's show said they were not aware of the controversy surrounding his comments.

But audience member Ann Frechette from Tampa Bay, Fla., said Tuesday night's jokes were “very harsh, very unlike David Letterman.”

She also said that “his apology was just another joke.”

Another, Cindy Baldwin from Ogden, Utah, said "I don't think [Letterman] should make comments about anyone's daughter, whether she's 18 or 14."

Emily Dore contributed to this report.