(Updated at 12:00 p.m. ET with Palin response)
(CNN) - Late night comedian David Letterman, responding to criticism his recent joke about a member of Sarah Palin's family crossed the line, said on his show Wednesday night he is guilty of "poor taste."
But Letterman, who has been a critic of the Alaska governor, said the recent joke - that Palin's "daughter was knocked up by Alex Rodriguez" at a recent Yankees game - was in reference to 18-year-old Bristol Palin, not 14-year-old Willow who actually attended the baseball game with her mother last week.
"We were, as we often do, making jokes about people in the news and we made some jokes about Sarah Palin and her daughter [Bristol]... and 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.
"Am I guilty of poor taste? Yes. Did I suggest that it was okay for her 14-year-old daughter to be having promiscuous sex? No."
iReport.com: Share your thoughts on Palin/Letterman flap
Letterman's comments come a day after the former Republican vice presidential candidate called the joke "inappropriate" and "sexually perverted."
"Acceptance of inappropriate sexual comments about an underage girl, who could be anyone's daughter, contributes to the atrociously high rate of sexual exploitation of minors by older men who use and abuse others," she said in a statement, assuming the joke was in reference to Willow.
On his show Wednesday Letterman said he hoped he "cleared part of this up" and said Palin is welcome to be a guest on the program at any time.
Palin had also taken issue with an item on Letterman's recent "Top Ten List," in which he said one of the Alaska governor's activities in New York was to buy "makeup at Bloomingdale's to update her slutty flight attendant look."
"The only thing I can say about this is I kind of like that joke," Letterman said.
In an issued statement, Palin spokeswoman Meghan Stapleton said: "The Palins have no intention of providing a ratings boost for David Letterman by appearing on his show. Plus, it would be wise to keep Willow away from David Letterman."