Joe Biden has pledged to be “more mindful” about physical contact with women, hoping draw a line under a controversy that has cast a cloud over his expected White House bid.
The former US vice-president posted a video on Twitter saying he will in future respect personal space.
Mr Biden stressed he has only ever intended to build a “human connection”, rather than make anyone uncomfortable.
He has not yet announced whether he will join the 2020 Democratic field.
“Social norms are changing, I understand that, and I’ve heard what these women are saying,” the 76-year-old Biden said in a video that looked like it had been recorded in a mobile phone.
His statement follows accusations against him of unwelcome touching from four women in recent days.
Lucy Flores, a former Nevada state assembly member, last week said that Mr Biden had kissed her on the back of the head at a campaign event.
This week a second woman, Amy Lappos, said Mr Biden had rubbed noses with her at a fundraiser in 2009.
On Tuesday, Caitlyn Caruso, a 22-year-old former college student, told the New York Times that at an event three years ago Mr Biden rested his hand on her thigh “even as she squirmed in her seat to show her discomfort” and hugged her “just a little bit too long”.
A 59-year-old writer DJ Hill told the newspaper that at a fundraising event in 2012 Mr Biden put his hand on her shoulder and then started dropping it down her back, which made her “very uncomfortable”.
The reaction among Democrats has been mixed.
White House hopefuls Senator Elizabeth Warren and Senator Amy Klobuchar had called upon Mr Biden to answer the accusations.
But House of Representatives Speaker Nancy Pelosi defended Mr Biden, saying the allegations should not disqualify a presidential run.
In the wake of the controversy, a pro-Trump political action committee, the Great America, released a video titled “Creepy Joe Biden”.
The video, which uses cable TV footage of Ms Flores detailing her Biden encounter, suggests the former vice-president is setting a bad example for US children.