The Republican candidate initially sought to brush off the emergence of the footage from an Access Hollywood show with Billy Bush as nothing more than "locker room banter".
But amid a mounting storm of controversy over the comments, which were quickly denounced by leaidng Republicans, Mr Trump posted a video on his Facebook page in which he offered a second apology.
Read the full transcript:
“I've never said I'm a perfect person, nor pretended to be someone that I'm not. I've said and done things I regret, and the words released today on this more-than-a-decade-old video are one of them. Anyone who knows me knows these words don't reflect who I am. I said it, I was wrong, and I apologise. I've traveled the country talking about change for America, but my travels have also changed me.
"I've spent time with grieving mothers who have lost their children, laid-off workers whose jobs have gone to other countries, and people from all walks of life who just want a better future. I have gotten to know the great people of our country, and I've been humbled by the faith they've placed in me. I pledge to be a better man tomorrow and will never, ever let you down.
"Let's be honest: We're living in the real world. This is nothing more than a distraction from the important issues we're facing today. We're losing our jobs, we're less safe than we were eight years ago, and Washington is totally broken. Hillary Clinton and her kind have run our country into the ground.
"I've said some foolish things, but there's a big difference between the words and actions of other people. Bill Clinton has actually abused women and Hillary has bullied, attacked, shamed and intimidated his victims. We will discuss this more in the coming days. See you at the debate on Sunday.”
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