Senator John McCain, the 2008 Republican nominee for US president, has become the latest senior figure in the party to withdraw his endorsement of Donald Trump as more of the candidate’s offensive comments about women were aired in the US.

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The Arizona senator issued a statement declaring it “impossible to continue to offer even conditional support” for Trump, in the wake of leaked video and audio showing Trump boasting about making sexual advances toward women without their consent.

“Cindy and I will not vote for Donald Trump,” McCain said in a statement that included his wife. “I have never voted for a Democratic presidential candidate and we will not vote for Hillary Clinton. We will write in the name of some good conservative Republican who is qualified to be president.”

Shortly after McCain released his statement, Trump made a surprise appearance outside Trump Tower in New York City. Early on Saturday evening, the billionaire emerged from his skyscraper, where he had been in crisis talks and debate preparation all day, to greet a group of 100 ardent supporters who had been demonstrating outside the building since morning.

Trump shook his fist in the air, waved and pointed, without saying anything. He then went quickly back into the building. His appearance raised a huge commotion among those gathered on Fifth Avenue in midtown Manhattan, prompting cheers and chants of “Trump for president” and “USA! USA!”

One onlooker, Karen Stecher from Windsor, Canada, said: “It’s ridiculous. I’ve seen a crowd react to a star in LA but it wasn’t like this. This is like entertainment but it’s scary because of the anger and aggression.”

The appearance came as it emerged Trump had made similarly crude comments about his relationships with women in a series of interviews with the US “shock jock” Howard Stern. The Republican candidate reportedly bragged about sleeping with 24-year-olds, described a woman reaching the age of 35 as “checkout time” and described his daughter Ivanka as having “always been very voluptuous”.

On Saturday afternoon Trump’s wife, Melania, released a statement in which she said Trump’s comments in conversation with the Access Hollywood presenter Billy Bush were offensive but asked the American people to see that her husband had “the heart and mind of a leader”.

Reached with a request for comment about the mounting controversy surrounding her father’s campaign, Ivanka Trump hung up on the Guardian.

McCain, locked in a tough re-election battle in Arizona, condemned Trump’s comments after the release of the 11-year-old Access Hollywood recording on Friday but initially stopped short of rescinding his endorsement. As leading Republican officials launched an exodus from Trump in the 24 hours that followed, he faced quickly mounting pressure.

He missed the chance to show political courage. It’s too late, John McCain. The people of Arizona deserve better Anne Kirkpatrick, McCain opponent

In his statement on Saturday, he said he had “wanted to support the candidate our party nominated” and respect the Republican primary process.

“He was not my choice, but as a past nominee I thought it important I respect the fact that Donald Trump won a majority of the delegates by the rules our party set. I thought I owed his supporters that deference,” McCain wrote.

McCain’s Senate race could determine whether the Republican party maintains its precarious control of the chamber. Other Republicans who disavowed their support for Trump on Saturday included Senate candidates Kelly Ayotte of New Hampshire, Rob Portman of Ohio, and Joe Heck of Nevada.

Some Republicans formally called on Trump to step aside and allow his running mate, Indiana governor Mike Pence, to become the party’s standard-bearer with just 30 days left until election day. Such voices included John Thune of South Dakota, the third-ranking Republican in the Senate.

Democrats swiftly rejected the desertion of Trump by those who had endorsed him as political calculation – pointing out that Republicans had stood by the former reality TV star even as he disparaged Mexican immigrants, Muslims, prisoners of war, the disabled and the Gold Star parents of an Iraq war hero and repeatedly made crude statements about women.

“McCain made it clear a long time ago: he is no longer a straight-talking maverick,” Ann Kirkpatrick, the Democratic congresswoman challenging McCain for his seat, said in a statement. “He missed the chance to show political courage and lead. He failed that test. Now, it’s too late, John McCain. The people of Arizona deserve better.”

McCain was the first prominent Republican to criticize Trump’s continued insistence that the Central Park Five, five young African Americans wrongfully convicted of rape in New York City in 1989, were guilty.

Despite the fact that the men’s convictions were overturned by DNA evidence, Trump insisted on Friday that the five, whom he called for to be executed at the time, were still guilty, pointing out to CNN that the youths confessed at the time. Trump did not mention that they were beaten by police and that New York City paid a $41m settlement.

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On Saturday, Pence seemed to leave the crisis entirely in Trump’s hands. In a statement, Pence said: “As a husband and father I was offended by the words and actions described by Donald Trump in the 11-year-old video released yesterday.

“I do not condone his remarks and cannot defend them. I am grateful that he has expressed remorse.”

Pence seemed to suggest that much would depend on Trump’s performance in the second presidential debate, scheduled for Sunday in St Louis.

“We pray for his family,” he said, “and look forward to the opportunity he has to show what is in his heart when he goes before the nation tomorrow night.”

Paul Ryan addressed a crowd at a Republican event in Wisconsin, to boos and heckles from Trump supporters. The nominee had been invited to attend by the House speaker but in the wake of the controversy on Friday, Ryan rescinded this invitation.

On Saturday Ryan took to the stage, saying “there is a bit of an elephant in the room”. He then referenced his statement on the issue, in which he said he was “sickened” by Trump’s remarks, before making clear “that’s not what we are here to talk about today”.

The Clinton campaign remained silent throughout the day. The Democratic nominee will address the issue at Sunday’s presidential debate, a campaign official told the Guardian, as that forum will provide her with the largest possible audience.

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The thinking within Clinton’s campaign was to let Trump suffer the repercussions of being unendorsed en masse by members of his own party. Surrogates for the former secretary of state were also encouraged to temper their responses.

Clinton’s team was also certain Trump would remain the Republican nominee, the official said, it being too late to remove him from the ballot. The campaign has not yet shifted its resources in light of the leaked video and plans to move forward with the same battleground plan.

In Manhattan, Trump’s appearance outside Trump Tower drew enthusiastic responses from the nominee’s supporters. One, Joseph Conigliaro, said: “I was excited to see him. He came out of nowhere! Everyone was screaming.

“He made those comments when he was a businessman and a TV star. They mean nothing. People say a lot of things in private they wouldn’t say in public running for office. It’s freedom of speech. We weren’t paying him. He was in business.”

Another supporter, Anne ‎McLain, said: “I felt so excited. I appreciate it. I called him Mr President. He’s going to build a wall to look after our national security. He loves women. Regardless of what he said in a bar 10 years ago.”