Mike Pence Michael (Mike) Richard PenceButtigieg stands in as Pence for Harris's debate practice Trump argues full Supreme Court needed to settle potential election disputes Pence adviser knocks ex-staffer who criticized Trump on COVID-19 MORE on Monday dismissed reports that he would step down as Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's running mate after a damaging video pushed other Republicans to withdraw support for the GOP presidential nominee.

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"It's absolutely false to suggest that at any point in time we considered dropping off this ticket. It's been the greatest honor of my life," Pence said on CNN.

"These rumors just furrow around presidential campaigns. It really is remarkable," Pence added on "Fox & Friends."

Some observers began to question whether Pence would stay on the ticket after the video surfaced on Friday. The Indiana governor condemned Trump's lewd remarks toward women and withdrew from a campaign appearance with Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R) in Wisconsin over the weekend.

But Pence said Monday that Trump has shown true remorse for his comments, which included saying he could do anything he wanted to women because he is a "star."

"I encouraged him to express what I believe is his sincere, personal remorse, and he did that Friday night. I wanted to give him time to show his heart on Sunday night. I thought he did that," Pence said on Fox.

"That kind of vulnerability and transparency is very moving to millions of Americans."

On Friday, The Washington Post revealed a 2005 recording of Trump discussing in vulgar terms how he can get away with unwanted advances on women because of his celebrity status.