CNN's Anderson Cooper, the debate's co-moderator, asked Trump whether he understood his remarks referenced sexual assault.
"No, I didn't say that at all," Trump said. "I'm not proud of it. I apologize to my family. I apologize to the American people. Certainly I'm not proud of it. But this is locker room talk."
The recording, taped by NBC's "Access Hollywood," was first published by The Washington Post on Friday. It includes a number of sexist remarks made by the Republican candidate that sparked uproar over the weekend, including descriptions Trump made about kissing women without consent and grabbing their genitals.
"When you're a star they let you do it," Trump can be heard saying.
The release of the video led several Republican Party members to pull their support of Trump.
"I was embarrassed by it," Trump said early during the presidential debate. "But I have tremendous respect for women."
Trump's campaign manager Kellyanne Conway defended her boss late Sunday on CNN, saying people "really should stop using" the phrase "sexual assault" to describe Trump's remarks.
"He did not say the word sexual assault," Conway said, adding that Trump "respects women."
"This is a man I've been alone with many times who's never been anything but gracious and gentleman," Conway said.
Trump isn't the only one facing scrutiny for failing to acknowledge sexual assault. When asked, Republican National Committee communications director Sean Spicer told the Weekly Standard in an interview
, "I don't know. I'm not a lawyer."
He later clarified by tweeting, "While I was asked question about a matter of law, it is never appropriate to touch anyone in an unwelcome manner."
Sen. Jeff Sessions, a Trump supporter who was US attorney in Alabama for 12 years and state attorney general for two years, also said the language Trump used did not describe sexual assault.
"I don't characterize that as sexual assault," Sessions told the Weekly Standard
in an interview. "I think that's a stretch."