By Jeremy Diamond CNN

NEW YORK (CNN) -- Donald Trump will "never" drop out.

The embattled Republican presidential nominee told a pair of newspapers on Saturday that he has no intention of quitting the presidential race despite a growing chorus of Republicans urging him to step aside in the wake of sexually aggressive remarks he made in 2005.

"I'd never withdraw. I've never withdrawn in my life," Trump told The Washington Post. "No, I'm not quitting. I have tremendous support."

He also told The Wall Street Journal there is "zero chance I'll quit."

Trump struck the defiant tone on Saturday less than 24 hours after previously unaired footage of Trump having talking in lewd and sexually aggressive terms about women during a 2005 taping for "Access Hollywood" surfaced.

In that timespan, Republicans have quickly condemned Trump for the comment many of them have deemed "inexcusable" and "indefensible," prompting Trump to issue his first-ever apology of his nearly 16-month campaign.

But Trump also signaled a willingness to fight, quickly turning from apology to defiant combativeness in the 90-second video, pivoting to attacking Democratic nominee Hillary Clinton for her husband's sex scandals.

The brash billionaire's insistence to the pair of newspapers on Saturday morning, though, came as Republican members of congress began urging Trump to step aside, with several senators who had endorsed Trump, including Sen. Mike Crapo of Idaho and Sen. Kelly Ayotte of New Hampshire, formally pulling their support.

Late Saturday morning, a campaign source told CNN Trump's running mate, Indiana Gov. Mike Pence, has decided not to attend a Wisconsin political event this afternoon hosted by House Speaker Paul Ryan.

A campaign source told CNN "Wisconsin is off" for Pence. The source said the decision was made this morning. No reason was given by the source.

Ryan, who said he was "sickened" by Trump's comments, announced Friday night that the GOP presidential nominee would no longer attend a Republican event in Wisconsin at which the two were slated to appear on Saturday. Multiple sources told CNN that Trump was asked not to come by Ryan, and one source said the message was delivered via intermediaries.

Trump's campaign had said Pence would represent him instead while the real estate magnate focuses on debate prep.

Around noon on Saturday, it was announced Pence would not be attending the Wisconsin event.

TM & © 2016 Cable News Network, Inc., a Time Warner Company. All rights reserved.