Donald Trump's lewd videotaped remarks about women threw his White House campaign and the Republican Party in crisis Saturday, just 30 days from the election and on the eve of his second debate with rival Hillary Clinton.

Trump nevertheless rejected growing calls from elected members of his own party to step aside over the 2005 remarks, insisting there is "zero chance I'll quit" the presidential race.

"We'll remember this day for a long time," David Gergen, who has served as adviser to four US presidents, told CNN. "A civil war is breaking out in the Republican ranks."

In the early evening hours a defiant Trump stepped outside of his Trump Tower skyscraper in New York, brandishing his fist in the air to cheers from dozens of supporters.

Asked if he was staying in the race, he responded: "100 percent."

Trump's own wife Melania said she was offended by her husband's "unacceptable and offensive" comments, which were caught on a hot mic just months after the two married -- the real estate magnate's third marriage -- boasting about his ability to grope women as he pleases.

But she urged American voters to accept his apology and support him.

"I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world," Melania Trump said in a statement.

The videotape, released Friday by The Washington Post, forced a rare apology from a campaign already peppered by controversies over Trump's treatment of women, roiling his Republican Party.

The Republican National Committee appeared to have halted part of its "Victory" program to elect Trump, with the RNC asking a vendor to "put a hold" on mail production, the Politico news website reported.

CNN said the RNC was considering ending a joint fundraising agreement with the Trump campaign.

Trump called the disclosure a "distraction," defiantly attacking the Clintons for husband Bill Clinton's past infidelities, and hinting strongly he would say more on the topic during Sunday's debate in St Louis, Missouri.

He denied his campaign was in crisis and predicted the controversy would blow over.

"The media and establishment want me out of the race so badly - I WILL NEVER DROP OUT OF THE RACE, WILL NEVER LET MY SUPPORTERS DOWN! #MAGA," he said on Twitter.

The hashtag refers to his campaign slogan: "Make America great again."

- 'Sickened' -
Republican reaction to the videotape came fast and furious, with some calling on the bombastic billionaire to step aside, or allow running mate Mike Pence to take the top of the ticket, others simply withdrawing their endorsement.

Pence, the governor of Indiana, said that as a husband and father he was "offended" by Trump's remarks.

House Speaker Paul Ryan, the top Republican officeholder, said he was "sickened" by Trump's comments, and disinvited him from a political event in Wisconsin. Pence was to go in Trump's place, but he canceled without explanation.

By Saturday, nearly a dozen senators, a dozen members of the House of Representatives and three governors -- all Republicans -- had withdrawn their support.

Among senior party figures, Condoleezza Rice -- a former secretary of state and national security advisor under president George W. Bush -- said "Enough! Donald Trump should not be President. He should withdraw."

Senator John McCain, the 2008 presidential nominee with whom Trump has sparred repeatedly, said "Donald Trump's behavior... make(s) it impossible to continue to offer even conditional support for his candidacy."

Governor John Kasich of Ohio, a former Trump adversary in the Republican primaries, said Trump's comments were "disgusting" and that "our country deserves better."

Illinois Senator Mark Kirk called for an "emergency replacement."

But top Trump surrogate Rudy Giuliani, a former New York mayor, insisted that "there is nothing that would cause his dropping out."

"That is wishful thinking of the Clinton campaign and those people who have opposed him for a long time. He is in the race to win," Giuliani added.

- Campaign in crisis -
With the November 8 elections one month away and Clinton leading in the polls by nearly five percentage points nationally, the latest uproar has plunged Trump in the deepest crisis of his turbulent campaign.

He had already been seriously hurt by a sloppy performance in his first debate with Clinton on September 26, a damaging Twitter war against a former Miss Universe and reports he may have paid no income taxes for 18 years.

Clinton, who is seeking to become the nation's first female commander-in-chief, is almost certain to call out Trump about the videotape during the debate.

"This is horrific," she said on Twitter. "We cannot allow this man to become president."

In the video, Trump uses vulgar and predatory language as he describes hitting on a married woman and grabbing women's crotches.

The three-minute video captures Trump reacting to an actress he was about to meet as he arrived on the set of daytime soap opera "Days of Our Lives," for the taping of a segment in which he was to have a cameo appearance.

"I've gotta use some Tic Tacs (breath mints), just in case I start kissing her," Trump says to Billy Bush, then host of the "Access Hollywood" show about celebrities.

"You know I'm automatically attracted to beautiful. I just start kissing them. It's like a magnet," he says.

"I don't even wait. And when you're a star they let you do it. You can do anything."

Trump also is heard bragging about trying to have sex with a woman he knew to be married.

Tic Tac rebuked the comments, saying: "Tic Tac respects all women. We find the recent statements and behavior completely inappropriate and unacceptable."