Letterman, 62, made the confessions to the audience during a taping of "The Late Show" for broadcast Thursday night, according to a statement by Worldwide Pants Inc., Letterman's production company.

"This morning, I did something I've never done in my life," Letterman told his audience, according to the statement. "I had to go downtown and testify before a grand jury."

During that testimony, Letterman acknowledged unspecified sexual relationships with staff members, the Worldwide Pants statement said.

"My response to that [allegation of sexual relationships] is, 'Yes I have.' Would it be embarrassing if it were made public? Perhaps it would," Letterman said. "I feel like I need to protect these people. I need to certainly protect my family."