US Republican presidential nominee Donald Trump said on Saturday he would never drop out of the race despite mounting bipartisan condemnation of his lewd and sexually aggressive comments about women in 2005.

Republican US presidential nominee Trump is seen in a video screengrab as he speaks during a statement and apology released via social media. [Photo/Agencies]

"I'd never withdraw. I've never withdrawn in my life," said Trump in an interview with The Washington Post, adding that he had "tremendous support."

Even his running mate Mike Pence said he was "offended" by Trump's lewd remarks about women.

"I do not condone his remarks and cannot defend them," Pence said in a statement, adding that Trump's 2nd debate Sunday night with his rival Hillary Clinton was an opportunity "to show what is in his heart."

Trump's defiant tone came hours after US House Speaker Paul Ryan joined other Republican leaders in their condemnation of lewd comments about women made by Trump.

"I am sickened by what I heard today. Women are to be championed and revered, not objectified," Ryan said in a statement.

"I hope Mr. Trump treats this situation with the seriousness it deserves and works to demonstrate to the country that he has greater respect for women than this clip suggests." '

In a leaked audio clip recorded in 2005, Trump made lewd remarks about an unidentified married woman he hoped to have sex with, boasted about how easy it is to attract women with his celebrity status and even talked about groping women.

When you're a star, women let you do anything, he was recorded as saying.

The New York billionaire later apologized for the "locker room banter" in the audio, but claimed that his Democratic rival Hillary Clinton's husband, former President Bill Clinton, "has said far worse to me on the golf course -- not even close."

However, Trump's bid to shift the focus seems to have failed as the chair of the Republican National Committee, Reince Priebus, together with a number of other influential Republican lawmakers, released statements blasting the billionaire. Some of them even urged Trump to quit the presidential race.

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