Donald Trump's wife has blasted lewd remarks about groping women shortly after he married her in 2005 as "unacceptable and offensive," but urged the public to accept his apology.

"The words my husband used are unacceptable and offensive to me. This does not represent the man that I know," Melania Trump said in a statement.

"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."

Trump made the comments while married to her and while she was pregnant with their first child together.

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Her comments come as Trump has vowed not to drop out of the US presidential race, after the vulgar comments he made about women were made public.

The Republican presidential nominee told The Wall Street Journal there is "zero chance I'll quit."

"I'd never withdraw. I've never withdrawn in my life," he said.

Trump claimed that he has been getting "tremendous support" following the leak of the controversial comments.

After posting a midnight "apology" video, Trump posted a tweet that can only be described as a drastic understatement of the controversy that has consumed his presidential campaign.

Trump also used the video as a forum to attack the Clintons, accusing the former president of "abusing women" as he apologised over a leaked recording exposing his own lewd comments about women.

Trump apologised for the remarks but spent little time grovelling, instead using the opportunity to attack his opposition.

"I said it, I was wrong, and I apologise," Trump told CNN News on Saturday.