“It’s completely inappropriate,” Ms. Flores said of Mr. Biden’s behavior with women. “And that is something that we should consider when we’re talking about the background of a person who is considering running for president.”

She first leveled her charges in an essay published on Friday in New York magazine’s The Cut. Ms. Flores, a candidate for lieutenant governor of Nevada in 2014, said that when Mr. Biden visited that year to campaign for her and other Democrats, he came up behind her before the rally, put his hands on her shoulders and planted “a big slow kiss” on the back of her head.

Ms. Flores said she felt compelled to come forward now because she believed Mr. Biden’s behavior with women was being left out of political conversations as he prepares for a possible presidential run.

Mr. Biden has drawn attention in the past for his intimate touching of political allies, their family members and even supporters he has just met — gestures that are seen as excessive to the point of creepy by some but viewed as harmless by his defenders.

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Mr. Biden’s allies said he often drew close to people he sensed were nervous before they went on stage in an effort to relax them, suggesting that is what he was doing with Ms. Flores. On Sunday night, Stephanie Carter, the wife of former Defense Secretary Ashton Carter, said Mr. Biden had been doing exactly that in 2015 when the vice president was memorably photographed holding her shoulders at Mr. Carter’s swearing-in ceremony.

“Joe Biden in my picture is a close friend helping someone get through a big day, for which I will always be grateful,” Ms. Carter wrote on Medium, adding that she wanted to reclaim an important day for her family “from strangers, Twitter, the pundits and the late-night hosts.”

And, in recognition of the political peril the former vice president now finds himself in, Mr. Biden’s female aides and supporters rushed to his defense over the weekend, some of them citing anecdotes about when he, for example, offered to get coffee himself when a male colleague asked one of his female aides to do it.