Indiana Gov. Mike Pence, Donald Trump’s running mate, on Monday shot down news reports that said he was thinking about jumping ship over the lewd remarks that the New York business made about women over a decade ago.

The Indianapolis Star and other news outlets reported ahead of Sunday’s debate that Mr. Pence was keeping his options open just in case Mr. Trump turned in a poor performance in his second debate showdown with Hillary Clinton.

“That was absolutely false,” Mr. Pence said on “Fox & Friends.” “These rumors just furrow around presidential campaigns. This is the first time I have ever been at this level, but it really is remarkable.”

Mr. Pence said the real story is that Mr. Trump won the debate in St. Louis.

“He showed humility, he showed strength, he expressed genuine contrition for the words that he used in the video that became public, and then he moved directly into the choice that the American people are facing, and it is such a dramatic choice,” Mr. Pence said. “I thought before the end of that 90 minutes, the American people could see the opportunity that we really have to change the direction of this country.”

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