Mr Trump said that “these words don’t reflect who I am… I apologise”.
In the video, Mr Trump says “you can do anything” to women “when you’re a star” and brags about trying to grope and kiss women.
Top Republicans condemned the comments. His election rival Hillary Clinton called them “horrific”.
“We cannot allow this man to become president,” she posted on Twitter. “I’ve said and done things I regret,” he said. “Anyone who knows me knows these words don’t reflect who I am. I said it, I was wrong, and I apologise.
“I’ve never said I’m a perfect person nor pretended to be someone I’m not. I pledge to be a better man tomorrow.”
However, he also tried to deflect the impact by attacking former President Bill Clinton.