The real estate mogul drew fire for the comments in which he gloated about what he could do because he was a "star."
"I never said that I'm a perfect person, nor pretended to be someone that I'm not," he said on the video, posted to his Facebook page.
"Anyone who knows me knows these words don't reflect who I am," he added. "I said it, I was wrong and I apologize."
Trump called the 2005 video a "distraction," noted that it was a "more-than decade-old video" and promised to be a "better man." But he also took aim Bill Clinton and the former president's record with women, without elaborating.
In the video, first reported by the Washington Post, Trump can be heard making the controversial remarks.
"You know I’m automatically attracted to beautiful -- I just start kissing them. It’s like a magnet. Just kiss. I don’t even wait," Trump says on the tape.
"And when you’re a star they let you do it... You can do anything."
"Whatever you want," another voice can be heard saying.
"Grab them by the p----," Trump says. "You can do anything."
Trump then can be heard bragging about how he tried to have an affair with a married woman.
"I moved on her and I failed. I’ll admit it," Trump said.
"I did try and f--- her. She was married," he can be heard saying.
"I moved on her like a b----, but I couldn’t get there. And she was married."
In the wake of the tape's release, Trump issued a statement dismissing the remarks as "locker room banter" and said he apologized if the remarks "offended" anyone.
The comments provoked a flurry of criticism from Republicans and Democrats alike and even led to Utah Rep. Jason Chaffetz pulling his vote.
ABC News did not immediately receive a response from NBC Universal, which owns "Access Hollywood." Bush has apologized for the incident.