NEW YORK/LOS ANGELES - David Letterman apologized on Monday for making a sexually charged joke about one of Alaska Gov. Sarah Palin's teenage daughters, as a group of Palin supporters planned a rally demanding the late-night TV show host be fired.

I told a joke that was beyond flawed, and my intent is completely meaningless compared to the perception of the joke by viewers, he said during Monday's taping of Late Night with David Letterman, according to a transcript given to Reuters.

And since it was a joke I told, I feel that I need to do the right thing here and apologize for having told that joke, he said. It's not your fault that it was misunderstood, it's my fault.

Last Tuesday, Letterman joked that New York Yankees slugger Alex Rodriguez had knocked up the former vice-presidential nominee's daughter during a family trip to a baseball game.

But the daughter in question was 14-year-old Willow, not the intended target, 18-year-old unwed mother Bristol. Letterman said the following night that he was confused between the two and would never make sexual jokes about a 14-year-old.

Despite his explanation, Palin has charged that Letterman made sexually perverted comments.

In the transcript from Monday's show, Letterman also said he was sorry to Palin and both her daughters.

I would like to apologize especially to the two daughters involved, Bristol and Willow, and also 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, he said.

The apologies came as a group of Palin supporters, calling themselves, planned a Tuesday protest outside the show's studio at the Ed Sullivan theater in New York's Times Square.

Palin and protest organizers, including Republican New York State Assemblyman Brian Kolb, have said the comments were demeaning to women, and they are comparing Letterman's case to that of radio host Don Imus, who was fired from CBS radio for offensive comments about a black women's basketball team.

Representatives for Palin on Monday were not immediately available to comment on Letterman's apology.

(Editing by Bob Tourtellotte)