"Enough! Donald Trump should not be President," the former Secretary of State said in a Facebook posting. "He should withdraw." Rice did not endorse Hillary Clinton, saying on that "as a Republican, I hope to support someone who has the dignity and stature to run for the highest office in the greatest democracy on earth."
John Kasich:
The Ohio Governor and previous Republican presidential hopeful said: "Nothing that has happened in the last 48 hours is surprising to me or many others. Many people were angry and questioned why I would not endorse Donald Trump or attend the Republican Convention. I've long had concerns with Donald Trump that go beyond his temperament. It's clear that he hasn't changed and has no interest in doing so. As a result, Donald Trump is a man I cannot and should not support."
Arnold Schwarzenegger:
The former Governor of California said: "For the first time since I became a citizen in 1983, I will not vote for the Republican candidate for President."
Trump's latest comments, from a hot microphone during the taping of a 2005 TV appearance, were the final straw for McCain, whose wife, Cindy, has devoted much of her time in the family foundation to women's rights, particularly abuse of women in Third World nations.
McCain now joins the entire Bush family and Mitt Romney in not supporting Trump, meaning the party's presidential nominees in 1988, 1992, 2000, 2004, 2008 and 2012 do not back Trump.
Congresswoman Martha Roby - who represents a strongly Republican district in Alabama - said she could no longer vote for Trump and she urged him to step down.
"As disappointed as I've been with his antics throughout this campaign, I thought supporting the nominee was the best thing for our country and our party," Roby said in a statement. "Now, it is abundantly clear that the best thing for our country and for our party is for Trump to step aside and allow a responsible, respectable Republican to lead the ticket."
Roby is one of at least eight Republican members of Congress to directly call for Trump to step aside, with former presidential candidates George Pataki, Jon Huntsman and Carly Fiorina.
Often in cutting off support for Trump these Republicans have rallied around Trump's running-mate, Indiana Governor Mike Pence. Senator Kelly Ayotte, tweeted that she would not vote for Trump and would instead write in Pence.
Pence said that he was "offended by the words and actions described by Donald Trump" but that he was grateful Trump "expressed remorse and apologised to the American people".
Trump said that he would not drop out of the race under any circumstances.
"I'd never withdraw. I've never withdrawn in my life," Trump said in a phone call from his home in Trump Tower in New York. "No, I'm not quitting this race. I have tremendous support."
"People are calling and saying, 'Don't even think about doing anything else but running," Trump said when asked about GOP defections. "You have to see what's going on. The real story is that people have no idea about the support. I don't know how that's going to boil down but people have no idea about the support."
With just a month until Election Day, experts say it would be logistically nearly impossible for the Republican Party to replace its nominee, and many Republicans seem to be waiting to see what happens in the coming hours.