Letterman said he believed it began when he called to ask Winfrey to appear on "Late Show" when he was going to do some shows in Chicago and Winfrey would not agree to appear.
Winfrey said she declined because she had been on Letterman's show before and there were drunk people in the audience who made it uncomfortable.
"I didn't want to have that experience again," she said. "That's really all it was for me."
Letterman said he didn't remember that appearance and was sorry for what Winfrey went through. He took her hand and kissed it. "I hope we can put this behind us, Oprah," he said.
"Let us do it, David," she said.
Despite Letterman's often withering comments about his NBC rival Leno, he said they were friends before Leno was picked over Letterman to be "Tonight" show host. Letterman believes they are still friends.
"He is the funniest guy I've ever known," Letterman said. "Just flat out, if you go to see him do his nightclub act, just the funniest, the smartest, a wonderful observationalist and very appealing as a comic. Therefore, the fact that he is also maybe the most insecure person I have ever known ... I could never reconcile that."
Letterman said some of the trash-talking between the two is simply the way comics often act toward one another.
Bruce Bobbins, a Leno spokesman, said Monday the NBC comic had no comment on Letterman's interview.