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ROUGH CUT (NO REPORTER NARRATION) STORY: U.S. presidential nominee Donald Trump vowed on Saturday to remain in the race even as his campaign was thrown into crisis as both his wife and running mate criticized him and more than a dozen prominent Republicans withdrew support and urged him to drop out following news of a recording of him making lewd comments. The Republican nominee briefly emerged from Trump Towers in New York on Saturday afternoon, to wave to a crowd of supporters gathered outside and exchange 'high fives.' Earlier on Saturday afternoon he wrote on social media website Twitter saying: "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!" The video was the latest calamity for Trump, who had hoped to revive his flagging campaign in the face of a recent drop in polls with less than a month until Election Day. Trump is due to appear alongside Democrat Hillary Clinton on Sunday night in their second debate in the runup to the general election. Clinton is not expected to address Trump's video before then. The 2005 video of Trump talking on an open microphone showed the then-reality TV star speaking openly about groping women and trying to seduce a married woman. The video was taped only months after Trump married his third wife, Melania. In a statement, Melania Trump called her husband's words "unacceptable and offensive to me." "This does not represent the man that I know," Melania Trump said. "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 backlash against the video was swift and widespread. More than 60 prominent Republican current and former officeholders issued statements condemning Trump's remarks about women, including more than 20 who called for him to end his presidential bid. In an unusual move, vice presidential running mate Mike Pence issued a critical statement of Trump's words, saying on Twitter that he "cannot defend them." "As a husband and father, I was offended by the words and actions described by Donald Trump," said Pence, who is governor of Indiana. Pence indicated he would continue to support Trump, despite calls from several Republicans that the New York real estate mogul step aside and let Pence be the nominee. There is no precedent for a major party to replace its nominee this late in the campaign and it is unclear if there is an avenue to force him out. Voting has begun in several states, including the important swing states of Virginia and North Carolina.