David Jackson

USA TODAY

ST. LOUIS – Donald Trump vowed Saturday to "never" drop out of the presidential race, even as a parade of Republicans called on him to do just that in the wake of sexually aggressive comments about women on a leaked video tape.

"The media and establishment want me out of the race so badly - I WILL NEVER DROP OUT OF THE RACE," Trump tweeted at mid-day Saturday. "WILL NEVER LET MY SUPPORTERS DOWN!"

He made his announcement after huddling with advisers at Trump Tower, a day after revelations that threw their presidential campaign into turmoil and inspired a rare apology from the New York businessman.

"I've never said I'm a perfect person, nor pretended to be someone I'm not," Trump said in a video statement and Facebook posting addressing the incident. "I've said and done things I regret, and the words released (Friday) on this more than a decade-old video are one of them."

Trump added: "I said it, it was wrong, and I apologize."

Donald Trump's apology for his 2005 video comments (full transcript)

Trump apologizes for video bragging about groping women

That 2005 tape — in which Trump talks about being able to "do anything" to women because he is wealthy and says he often kisses and grabs them without warning — set off what may be an existential crisis for his campaign.

A steady stream of Republicans began to call for Trump to step aside as nominee.

The list ranges from former Secretary of State Condoleezza Rice to Rep. Barbara Comstock of Virginia to Sen. John Thune of South Dakota to former Utah governor Jon Huntsman to once-supportive radio talk show host Hugh Hewitt, who tweeted: "For the benefit of the country, the party and his family, and for his own good, @realDonaldTrump should withdraw. More and worse oppo coming."

Here is the list of Republicans who are not supporting Trump

Another prominent Republican — Sen. John McCain of Arizona, the party's 2008 presidential nominee — said recent events have made it "impossible to continue to offer even conditional support for his candidacy."

Melania Trump, the candidate's wife, said that while his words are "unacceptable and offensive to me," they do not reflect the man she knows. "I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world," she said in a statement put out by the campaign.

"The words my husband used are unacceptable and offensive to me. This does not represent the man that I know. He has the heart and mind of a leader. I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world. "

The Republican nominee and Democratic rival Hillary Clinton are scheduled to meet for a second debate on Sunday in St. Louis.

House Speaker Paul Ryan, R-Wis., who was supposed to have campaigned with Trump on Saturday, said the businessman's comments "sickened" him, and added that "women are to championed and revered, not objectified."

Ryan announced that Trump was "no longer attending" a planned campaign event in Wisconsin.

First Trump-Ryan appearance derailed by Trump tape

Trump said that, rather than travel to Wisconsin, he would engage in debate preparation in New York with supporters — including Republican National Committee Chairman Reince Priebus, who issued a terse statement of his own condemning Trump's comments.

"No woman should ever be described in these terms or talked about in this manner," Priebus said. "Ever."

After his meetings, the candidate wandered outside of Trump Tower to greet supporters who gathered to express support. The crowd chanted "U-S-A! U-S-A!"

While many Democrats sat back and enjoyed the spectacle of Trump and his sexually aggressive comments about women, Clinton tweeted that "this is horrific. We cannot allow this man to become president."

The Washington Post reported that Trump made his comments during a chat with Billy Bush, then a host of Access Hollywood, before taping a segment for the program in 2005.

"You know, I'm automatically attracted to beautiful (women) — I just start kissing them," Trump said at one point, apparently unaware he was being taped. "It's like a magnet. Just kiss. I don't even wait."

He added: "And when you're a star, they let you do it. You can do anything ... Grab them by the p----y. You can do anything."

On the tape, Trump also talked about "moving on" a married woman — a colleague of Bush's — but being rebuffed. He makes reference to the woman's "fake" breasts, but uses a different term.

“I moved on her like a b----, but I couldn’t get there. And she was married,” Trump says. “Then all of a sudden I see her, she’s now got the big phony t---s and everything. She’s totally changed her look.”

Bush, who now works with NBC's Today show, issued a statement apologizing for his sexual bantering with Trump. Bush — the nephew of former president George H.W. Bush and a cousin of ex-president George W. Bush — said he is "embarrassed and ashamed" by the Trump tape. “It’s no excuse, but this happened 11 years ago," he added. "I was younger, less mature and acted foolishly in playing along. I’m very sorry.”

Billy Bush 'sorry' and 'ashamed' of role in lewd talk in Trump audio

Trump's comments about groping women draw swift condemnation

Critics called Trump's comments vulgar at best, and some said the comment about grabbing women amounted to promotion of sexual assault.

Jeb Bush, who lost to Trump in the Republican primaries earlier this year, said in a tweet: "As the grandfather of two precious girls, I find that no apology can excuse away Donald Trump's reprehensible comments degrading women."

In his statement, Trump said that campaigning across the nation has "changed" him, and he pledged to be a "better man" because of it.

The New York real estate magnate also called the flap "a distraction" from the important issues.

"We are losing our jobs," Trump said. "We are less safe than we were eight years ago and Washington is broken. Hillary Clinton, and her kind, have run our country into the ground."

Trump also cited women who alleged sexual misconduct against former president Bill Clinton, and claimed that "Hillary has bullied, attacked, shamed and intimidated his victims. We will discuss this more in the coming days."

During the day, Trump re-tweeted posts from Juanita Broaddrick, who accused Bill Clinton of a sexual assault decades ago. In one tweet, she said: "Hillary calls Trump's remarks 'horrific' while she lives with and protects a 'Rapist.' Her actions are horrific."

GOP strategists said they worried that the Trump revelations could hurt other Republicans on the Nov. 8 ballot. Republicans are defending 24 Senate seats to Democrats’ 10, and are locked in tight races from North Carolina to Nevada.

Rob Engstrom, the senior vice president of the U.S. Chamber of Commerce, on Friday night called on Trump to “step down immediately” and hand the nomination to his running mate, Indiana Gov. Mike Pence. The chamber launched a “Save the Senate” campaign in late May to encourage Republican donors, who were avoiding the divisive presidential campaign, to rally around competitive Senate races.

South Carolina Sen. Lindsey Graham, a frequent Trump critic who serves as a fundraiser for the chamber’s Senate effort, warned Saturday that Trump's proposed use of Bill Clinton indiscretions could be a losing strategy.

“I don’t believe the Bill Clinton defense will work as we impeached Bill Clinton,” Graham said on Twitter. “I was there.”

A number of Republicans also said the comments may well end whatever chance Trump himself had to prevail in the Nov. 8 election.

Matt Mackowiak, a Republican consultant based in Texas, said "the bombshell" confirms an existing narrative already hurting Trump with women who make up more than half the electorate.

"The bottom line is Trump has been misogynistic for much of his adult life," Mackowiak said, adding that "this will begin a death spiral for the Trump campaign and I don't know how you can break it. We don't know where his floor is now."

Liz Mair, a Republican consultant who participated in the "Never Trump" movement, called the whole thing entirely predictable.

"It's incredible that so many Republicans couldn't see that something like this would eventually come out," she said.

Contributing: Fredreka Schouten