US talk show host David Letterman admitted in his nightly program on Thursday to having sex with members of his staff, as he detailed an extortionist's efforts to relieve him of $2.0-million.

"I have had sex with women who work on this show," Letterman told a studio audience in New York which at times appeared unsure whether the confession was part of a skit.

The married 62-year-old said three weeks ago a package appeared in the back seat of his car from a person who demanded $2.0-million for keeping knowledge the flings secret.

Letterman went on to explain his decision to report the matter to the authorities, which led to testimony before a grand jury earlier that day. "I had to tell them all of the creepy things I had done," he said.

"Would it be embarrassing if it were made public? Perhaps it would, perhaps it would, and especially for the women," he joked.

"What you don't want is a guy saying: 'I know you had sex with women, I would like $2.0-million or I'm going to make trouble for you,' so that is where we stand right now."

He added that the person in question is under arrest.

Letterman, a doyen of the nightly chat shows that are immensely popular in the United States, earlier this month had President Barrack Obama as a guest, the first time a sitting president had appeared on the CBS show.