Former Nevada Assembly member, Lucy Flores says that at a campaign event, Mr Biden kissed her on the back of her head.

Another woman, Amy Lappos, said that ten years ago, Mr Biden acted rather inappropriately by touching her face with both of his hands and rubbing noses with her, too.

Although he has not announced his candidacy, the former Delaware senator – Joe Biden – is seen as a possible force to reckon with in the Democratic presidential nominations.

In 2014, the then vice-president – Mr Biden flew into Nevada to support Ms Flores as the Democratic candidate for lieutenant governor.

Mr Biden placed two hands on my shoulders from behind, she said. “I felt him get closer to me from behind. He leaned further in and inhaled my hair. I was mortified. He proceeded to plant a big slow kiss on the back of my head. My brain couldn’t process what was happening. I have never experienced anything so blatantly inappropriate,” she wrote.

But on Sunday, Mr Biden issued a statement himself. While reiterating he didn’t actually remember that to have happened, he vowed to “pay attention” to Ms Flores.

“In my many years on the campaign trail and public life, I have offered countless handshakes, hugs, expressions of affection, support and comfort. And not once – never – did I believe I acted inappropriately. But we have arrived at an important time when women feel they can and should relate their experiences and men should pay attention.” Joe Biden wrote in his statement.

But many supporters have risen to defend Mr Biden. One is the former aide to the vice-president – Cynthia Hogan telling the New York Times that “He treated us with respect and insisted that others do the same”.