David Letterman, the late night talk show host, said on his show on Thursday that he had been the victim of an extortion attempt over charges of sexual affairs with staff members, claims that he conceded were true.

Mr. Letterman said on “The Late Show,” on CBS, that he had been approached by a person who wanted $2 million not to go public with information that Mr. Letterman had been in sexual relationships with women who work on his show.

Mr. Letterman said that he had testified before a grand jury and had admitted to the relationships.

“My response to that is, yes I have. Would it be embarrassing if it were made public? Perhaps it would,” he said on the show. “I feel like I need to protect these people. I need to certainly protect my family.”

In March, Mr. Letterman, 62, married his longtime girlfriend, Regina Lasko, whom he had been dating for two decades. They have a son, now 6.