Indiana Gov. Mike Pence denied on Monday that he ever considered leaving the Republican presidential ticket following revelations from a leaked 2005 video that showed Donald Trump boasting about forcing himself onto women.

The Republican vice-presidential nominee told CNN that reports he considered leaving the race were "absolutely false," though he did not answer whether his wife, Karen Pence, was incensed by Trump's lewd comments.

"It's the greatest honor of my life to be nominated for vice president by my party. Look, politics is a tough business, I get that," Pence said.

Mike Pence: It is “absolutely false to suggest that at any point in time we considered dropping off this ticket” https://t.co/xeoWCPEkY8 — CNN Politics (@CNNPolitics) October 10, 2016

The Indiana governor reiterated that he was offended by Trump's bragging that he could grab women "by the p---y," and kiss women without permission because he was a celebrity. But the governor said he believed the real-estate magnate delivered a sincere apology over the weekend in multiple forums.

"As I said on Saturday, I couldn't condone, I couldn't defend those remarks. I encouraged Donald Trump on Friday to apologize for him. He did. He expressed his personal remorse. But I also encouraged him Saturday to take that to American people, to show them his heart," Pence said.

Pence praised Trump for "speaking boldly" during the second presidential debate on Sunday night, and slammed Hillary Clinton over her answer to a question about a private speech to people in the financial industry.

"Hillary Clinton, when she's confronted with speeches on Wall Street, gave us a one-minute speech on Abraham Lincoln and never answered the questions that were posed," Pence said.

Pence's comments come after a weekend in which many high-profile Republicans broke off their support for their party's presidential nominee in light of the 2005 video. Rumors also swirled about the Republican National Committee's involvement in boosting the campaign, and whether key members of Trump's campaign staff were also considering quitting.

In a tweet Monday morning, campaign manager Kellyanne Conway mocked media outlets for reporting that Pence was considering dropping out, despite earlier rumors that Conway herself may be considering leaving the ticket.