"Anyone who knows me knows these words don't reflect who I am. I said it, I was wrong and I apologize," Trump said in the video released Friday night.
He said he has been changed by the travels he has made and people he has met during the campaign.
"I pledge to be a better man tomorrow and will never ever let you down," he said.
Trump also attacked Bill Clinton for what he described as abuse of women and Hillary Clinton for her treatment of her husband's alleged victims.
"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."
US Republican presidential candidate Donald Trump blurted out lewd and sexually charged comments about women as he waited to make a cameo appearance on a soap opera in 2005.
In a conversation with Billy Bush, then a host of the television show "Access Hollywood, the celebrity businessman talk about his unacceptable action with a married woman which his remarks were caught by a live microphone that Trump didn't appear to know was recording their conversation.
In a statement released by his campaign, Trump said: "This was locker room banter, a private conversation that took place many years ago. Bill Clinton has said far worse to me on the golf course - not even close. I apologise if anyone was offended."
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