He adds seconds later: “Grab them by the p----. You can do anything.”

The one-sentence response from the head of Trump’s Republican Party was devastating.

“No woman should ever be described in these terms or talked about in this manner. Ever,” said Reince Priebus, who had stood by Trump through his past provocative comments.

So, too, were the words of House Speaker Paul Ryan: “I am sickened by what I heard today. Women are to be championed and revered, not objectified. I hope Mr Trump treats this situation with the seriousness it deserves and works to demonstrate to the country that he has greater respect for women than this clip suggests.”

Ryan added tartly that Trump was “no longer attending” a joint campaign appearance set for Saturday in Wisconsin.

Other Republicans, painfully aware of the possible impact on their own political fates, were quick to chime in. New Hampshire Senator Kelly Ayotte, who is locked in a close race, called the comments “totally inappropriate and offensive”.

Senate Majority Leader Mitch McConnell said the comments were “repugnant” and that Trump “needs to apologise directly to women and girls everywhere.”

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.

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.

Republican lawmaker Mike Coffman from Colorado told CBS that Trump should “step aside” and said “his defeat at this point seems almost certain.”

Trump’s running mate, Indiana Governor Mike Pence, was “beside himself” and his wife was furious, according to a person familiar with their thinking. That person spoke on the condition of anonymity, because they were not authorised to share the private discussion. In public, Pence ignored questions shouted by reporters in Rossford, Ohio, where he was campaigning with his daughter.

Access Hollywood said reports about Trump’s lewd behind-the-scenes comments as star of The Apprentice led it to dig through its archives and turn up the previously unaired footage from 2005. It was recorded during a bus ride while Trump was on his way to tape an episode of the soap opera Days of Our Lives.

Trump’s Democratic rival, Hillary Clinton, seized on Trump’s quotes, calling them “horrific.” She said in a Twitter message: “We cannot allow this man to become president”. But she had her own problems with revelations.

The WikiLeaks organisation posted what it said were thousands of emails from Clinton campaign chairman John Podesta, including some with excerpts from speeches she gave to Wall Street executives and others – speeches she has declined to release despite demands from Trump.

The excerpts include Clinton seeming to put herself in the free trade camp, a position she has retreated from. In a talk to a Brazilian bank in 2013, she said her dream was “a hemispheric common market, with open trade and open borders.”

Trump strongly opposes current US trade deals and insists Clinton is too cosy with Wall Street to reform it.

Friday’s revelations came two days before Trump and Clinton are to meet in Sunday’s second presidential debate, with the Republican urgently in need of a strong performance. After his uneven showing in the first contest, public opinion polls have showed Clinton pulling ahead in nearly all battleground states, some of which are already in the midst of early voting.

There were plenty of other problems for Trump on what surely was one of the worst days of his two-year drive for the White House.

His advisers planned for him to spend a quiet Friday preparing for the debate and meeting with border security officials. But the day was quickly consumed by a series of controversies, including Trump’s unsubstantiated claim about immigrants in the US illegally voting in the election and his questioning the innocence of five black teenagers exonerated in a 1989 rape case.

Then, there were new signs of unusual links between Trump and Russia. For the first time, the US publicly blamed the Russian government for hacking the Democratic National Committee and accused Moscow of trying to interfere with the American election. Diplomats also said Russia had lodged a formal complaint with the United Nations over a top UN official’s condemnations of Trump.

Also in the mix Friday: new questions about the Trump campaign’s finances. With roughly a month until Election Day, the campaign has yet to schedule the US$100 million in television advertising that his campaign boasted about just two weeks ago. The campaign has just half that amount scheduled, and late this week shifted ad money around rather than increasing its overall investment, suggesting a bit of penny-pinching even as the clock winds down.

While Trump has survived numerous controversies that would have sunk other candidates, Friday’s developments came at a crucial moment. Less than five weeks from Election Day, he needs to expand his support and is struggling in particular with minorities and women. The unearthed video of Trump’s 2005 comments can hardly help with female voters.

On the tape, Trump is caught on a live microphone while talking with Billy Bush of Access Hollywood. The candidate is heard saying “I did try and f--- her. She was married.” He also uses graphic terms to describe the woman’s body and says he frequently tries to kiss beautiful women.

In a statement after the tape was revealed, Trump called his comments “locker room banter” and a “private conversation that took place many years ago”.

“Bill Clinton has said far worse to me on the golf course – not even close,” he said. “I apologise if anyone was offended.”