As President Biden continued to work on Monday to tamp down Democratic calls for him to end his campaign, Gov. Gretchen Whitmer of Michigan, one of the most prominent officials whose name has been floated as an alternative, ruled it out.

Ms. Whitmer was asked in an interview with The Associated Press whether she would consider running in the hypothetical event that Mr. Biden stepped aside. She said no.

The speculation is “a distraction more than anything,” she said. “I don’t like seeing my name in articles like that because I’m totally focused on governing and campaigning” for the existing ticket of Mr. Biden and Vice President Kamala Harris.

Her office did not respond to a request from The New York Times to confirm her comments.

Ms. Whitmer is one of several governors who are widely believed to have ambitions to run for president in a future election, and who have been repeatedly named as possible candidates in the event that Mr. Biden ended his campaign, which he has said forcefully that he will not do.

Other Democratic governors who have been eyed nationally are making their support of Mr. Biden clear.

Nathan Click, a spokesman for Gavin Newsom of California, said Mr. Newsom had “addressed this repeatedly” as he campaigned for Mr. Biden in recent days. At an event in Michigan on Thursday, he said, “I don’t even like playing in the hypotheticals.”

Mike Ollen, an aide to Gov. J.B. Pritzker of Illinois, said similarly: “There’s no point in engaging in these hypotheticals. As Joe Biden has said, he is our nominee and J.B. remains all-in on defeating Donald Trump in November.”

And Manuel Bonder, a spokesman for Gov. Josh Shapiro of Pennsylvania, pointed to an interview last year in which the local news outlet KDKA asked Mr. Shapiro whether he would consider running if Mr. Biden didn’t. Mr. Shapiro said then, “The answer is no.”