US presidential candidate Donald Trump has said he will never drop out of the race to be president. He would never let his supporters down, he added.
Mr Trump has been under pressure after a tape from 2005 of him making obscene comments and bragging about groping and kissing women emerged on Friday.
He told the Wall Street Journal there was "zero chance I'll quit" and he was getting "unbelievable" support.
Top Republicans have condemned Mr Trump's remarks in the video.
Since the tape emerged, at least 10 Republican senators have either said they will not be voting for the Republican candidate in the general election in 30 days' time, or have called for him to stand aside.
The latest to join them is former Republican presidential candidate John McCain, who said Mr Trump's comments "make it impossible to continue to offer even conditional support for his candidacy".
And former Secretary of State Condoleezza Rice said: "Enough! Donald Trump should not be President. He should withdraw."
Mr Trump's election rival Hillary Clinton called the comments "horrific".
His running mate Mike Pence said he was "offended" by Mr Trump's video, but grateful he had expressed remorse and apologised to the American people.
"We pray for his family" he said in a statement.
In an exuberantly capitalised tweet, the Republican candidate said "the media and establishment want me out of the race so badly".
Mr Trump's wife Melania issued a statement on Saturday saying: "The words my husband used are unacceptable and offensive to me."
She said her husband had "the heart and mind of a leader".
In the recorded comments, which date back to 2005 when Mr Trump was appearing as a guest on a soap, he says "you can do anything" to women "when you're a star" and is heard saying "grab them by the pussy".
The candidate released a video statement apologising for the comments.
After some Republican lawmakers called on Mr Trump to step down as candidate, the billionaire told the Washington Post later on Saturday:
"I'd never withdraw. I've never withdrawn in my life."
Mr Trump's 2005 comments, posted by the Washington Post, overshadowed the release of transcripts of Mrs Clinton's speeches to private events, by the whistle-blowing site Wikileaks.
The candidate had married his third wife Melania a few months before the recording. She said on Saturday: "I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world."
On Saturday New Hampshire Senator Kelly Ayotte joined the long list of Republican members of Congress who have said they will not vote for Mr Trump.
"I cannot and will not support a candidate for president who brags about degrading and assaulting women," she said in a statement.
Ms Ayotte - who faces a competitive race for re-election - said she would not vote for Mrs Clinton but instead would "write in" Mr Pence, on her ballot paper.
Reports in the US media suggest that Mr Pence no longer plans to attend a campaign event in Wisconsin alongside House Speaker Paul Ryan.
Mr Ryan - the most senior elected Republican in the US - had originally invited Mr Trump to the event but rescinded his invitation, saying he was "sickened" by what he had heard. Mr Pence was due to go in his running mate's place.
Senators Mike Crapo of Idaho, Ben Sasse of Nebraska, Mike Lee of Utah, Dan Sullivan of Alaska and John Thune of South Dakota were among the elected Republicans calling on Mr Trump to abandon his candidacy.
Several governors and congressmen and women have rescinded their support for the candidate since the tape was published.
Which Republicans have deserted Donald Trump?
Former Republican California Governor Arnold Schwarzenegger also said he would not be voting for the Republican candidate.
Vice-President Joe Biden joined those condemning Mr Trump's comments. "Such behaviour is an abuse of power. It's not lewd. It's sexual assault," he tweeted.
"Women have the power to stop Trump," Mrs Clinton wrote on Twitter, and released a video featuring the latest audio, playing over footage of women and girls.
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.
But in his video apology, he attacked the former president directly:
"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."
Mr Pence said the debate would be an opportunity for Mr Trump "to show what is in his heart when he goes before the nation".
The day after a video emerged in which he suggested he could have any woman he wants because he's a star and so could just grab them by the pussy, Mr Trump is in a whole ocean of hot political water.
Enough, quite possibly, to sink any chance he had of winning the White House.
There is a violence in the phrases "grab 'em by the pussy" and "you can do anything" that any victim of abuse would recognise and that most women would find sickening.
But this tape doesn't just offend women, judging from the reaction in the Republican party. It has offended a lot of men too. Whether those men will now withdraw their endorsements of him is yet to be seen.