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 US election rival Hillary Clinton called them “horrific”.
“We cannot allow this man to become president,” she posted on Twitter. Mr Trump’s 90-second statement on Saturday morning appeared to be his first full apology in a campaign laced with controversial remarks.
“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.
Donald Trump has often found himself in hot water for public comments he’s made about women over the years. It turns out he’s said lewd and disparaging things in private as well. Go figure.
The videotape release comes at a most inopportune time for the Republican nominee, who was trying to use his running mate’s well-received debate performance on Tuesday to reboot his campaign after a week of distractions and controversy. On Wednesday he told a local news interviewer that his previous offensive comments about women – which have dogged his campaign since the first Republican primary debate last August – were made for the “purpose of entertainment”.
That explanation doesn’t fit with the boorish, newly married Trump shown on the video privately boasting about his efforts to seduce a married woman and have his way with whomever he pleases.
Now Mr Trump will enter Sunday’s debate with a new cloud hanging over his candidacy. It’s almost certain that one of the town hall participants will ask him about it. There may be no easy way to respond – but Mr Trump will have to find an acceptable answer. If he bungles it, nothing else he says during the 90-minute debate will matter.
“Bill Clinton has actually abused women, and Hillary has bullied, attacked and shamed his victims.
“We’ll discuss this in the coming days,” he said. “See you at the debate on Sunday.”
The second TV debate between Mr Trump and Mrs Clinton will take place on Sunday evening in St Louis.
Mr Trump recently said he would not bring up stories about Bill Clinton’s infidelities in the debate, after previously threatening to do so.