Vice presidential hopeful Mike Pence has no plans to drop out of the race for the White House despite recent reports and tension between the Indiana governor and his running mate, Donald Trump, Pence said Monday.

"It's absolutely false to suggest that at any point in time we considered dropping off this ticket," he told CNN. "It's the greatest honor of my life, to have been nominated by my party to be the next vice president of the United States of America."

Pence denied rumors that surfaced over the weekend after a 2005 recording of his running mate speaking in a vulgar way about women on the set of the soap opera "Days of Our Lives" was obtained and posted by The Washington Post.

"I'm automatically attracted to beautiful women — I just start kissing them, it's like a magnet. Just kiss," Trump said, in part. "I don't even wait. And when you're a star, they let you do it. You can do anything."

Trump repeatedly characterized the conversation with "Access Hollywood" host Billy Bush as "locker room banter" that he believed was private. The comments were caught on a hot microphone.

Pence issued a statement Saturday saying that he could not stand behind Trump's comments.

"I do not condone his remarks and cannot defend them," he said. "I am grateful that he has expressed remorse and apologized to the American people."

Relations between Trump and Pence appeared strained after Pence and Democratic vice presidential candidate Tim Kaine went head to head in a debate last week.

Although Pence's performance was generally considered stronger than Kaine's, unidentified campaign sources told CNBC and CNN that the GOP presidential nominee was upset that Pence's performance was considered better than his own and that Pence deflected sticky questions instead of defending Trump.

At a presidential debate Sunday, Trump appeared to confirm the rift between the pair when the GOP nominee brushed off Pence's Syria policy.

"He and I haven't spoken, and he and I disagree," Trump said.

Pence said on Monday that debate moderator Martha Raddatz asked a misleading question and he insisted that the pair had a cohesive foreign policy vision.

"He said we hadn't spoken specifically about what (Raddatz) said and the reason for that was because I didn't say that," he said with a laugh. "And I understand that. I look forward to catching up with him about it today."