WASHINGTON — Republican leaders began to abandon Donald Trump by the dozens Saturday after the release of a video showing him speaking of women in vulgar sexual terms, delivering a punishing blow to his campaign and plunging the party into crisis a month before the election.

Fearing his candidacy was on the verge of undermining the entire Republican ticket, a group of senators and House members withdrew their support for him Saturday, with some demanding that he step aside.

Foremost among them was Sen. John McCain of Arizona, the party’s 2008 nominee.

“I thought it important I respect the fact that Donald Trump won a majority of the delegates by the rules our party set,” McCain said in a statement. “But Donald Trump’s behavior this week, concluding with the disclosure of his demeaning comments about women and his boasts about sexual assaults, make it impossible to continue to offer even conditional support for his candidacy.”

And in an unheard-of rebuke by a running mate, Gov. Mike Pence of Indiana, the Republican vice-presidential  candidate, declined to appear on Trump’s behalf at a party gathering in Wisconsin and offered him something of an ultimatum Saturday afternoon.

Pence said in a statement that he was “offended by the words and actions described by Donald Trump” in the video and cast Trump’s second debate with Hillary Clinton, on Sunday, as an urgent moment to turn around the campaign.

“I do not condone his remarks and cannot defend them,” Pence said, adding, “We pray for his family and look forward to the opportunity he has to show what is in his heart when he goes before the nation tomorrow night.”

By Saturday evening, no fewer than 36 Republican members of Congress and governors who had not previously ruled out supporting Trump disavowed his candidacy.

Aides described Trump as shaken. Shortly after midnight, he released a statement, saying: “I’ve said and done things I regret, and the words released today on this more than a decade-old video are one of them.”

In a telephone interview Saturday, he shrugged off the calls to leave the race, saying he would “never drop out of this race in a million years.”

On Saturday afternoon, Sen. John Thune of South Dakota, chairman of the Republican conference, became the senior-most Republican to call on Trump to end his bid and make way for Pence.

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