Republican presidential nominee Donald Trump has vowed to remain in the race after prominent members of his party called for him to drop out following news of a recording of him making lewd comments about women.

Trump sought to do damage control early on Saturday morning in a hastily recorded apology, declaring himself a changed man and attempting to shift the focus to his opponent, Democrat Hillary Clinton.

Trump threatened, again, to focus his attacks on the infidelities of former President Bill Clinton, saying he would talk more about the pasts of both Clintons in coming days.

Trump has dismissed questions about his own martial infidelities as irrelevant.

Trump told the Wall Street Journal on Saturday morning "zero chance I'll quit."

Three Republican members of the Senate publicly announced they will not vote for Trump and former rival Carly Fiorina called on him to withdraw.

Disclosure of a 2005 video of Trump talking on an open microphone showed the then-reality TV star speaking openly about groping women and trying to seduce a married woman. The video was taped months after Trump married his third wife, Melania.

Trump took to Twitter on Saturday morning, seeming to make light of the controversy by posting on the online social media website "Certainly has been an interesting 24 hours!"

Trump has struggled to win over women voters, lagging Clinton in the polls.

"Anyone who knows me knows these words don't reflect who I am. I said it, I was wrong, and I apologise," Trump said in his video statement, posted on his Facebook page.

Trump's comments aired in a near-constant loop on US news programs on Friday.
"I did try and f*** her. She was married," Trump said about one woman, before discussing his attraction to others.

"I just start kissing them," he said. "And when you're a star they let you do it."

"Grab them by the p****. You can do anything," Trump said.

A stream of Republican leaders condemned the remarks and some withdrew their support for Trump.

US Representative Jason Chaffetz of Utah, who has been one of Clinton's fiercest critics, said he had retracted his endorsement of Trump, telling CNN he would not be able to look his 15-year-old daughter in the eye if he voted for Trump.

Martha Roby, a Republican member of Congress from the conservative state of Alabama, also withdrew her support.

"Donald Trump's behaviour makes him unacceptable as a candidate for president, and I won't vote for him," she said in a statement.

Utah's Republican Governor Gary Herbert said on Twitter he would also no longer vote for Trump. "Tonight, millions of Republicans are facing a moment of truth," Herbert said.

Other prominent Republicans indicated they would stick with Trump. Ralph Reed, head of the Faith and Freedom Coalition, and Tony Perkins, head of the conservative Family Research Council, both told news outlets they will continue to support Trump.

Representative Jack Kingston, a Republican from Georgia, argued that Trump has changed in the decade since the video was filmed.

"I think 10 years ago he was a different man than he is today, I am very glad that he quickly apologised," Kingston said.

But Republican strategist Ron Bonjean said "this feels like it is quickly becoming a political 'game over'" for Trump.

"Unless voters don't care about these issues or believe that this is simply political dirty tricks by releasing the videos now, Trump is going to have to pull a rabbit out of his hat in order to turn things around," Bonjean said.