This article is more than
5 year oldBut he needs to understand that "people's space is important", the House of Representatives Speaker added.
A second woman has levelled accusations as Mr Biden ponders a run for the White House in 2020.
Mr Biden has said he does not believe he has ever acted inappropriately.
The latest comes from Amy Lappos - a 43-year-old former aide to a Democratic congressman.
She says Mr Biden touched her inappropriately at a fundraiser in a private home in Hartford, Connecticut, in 2009.
She told the Hartford Courant the then vice-president entered the kitchen to thank a group of aides, before wrapping both hands around her face and pulling her in to rub noses.
Ms Lappos called on Mr Biden not to run for the White House, saying: "Uninvited affection is not okay. Objectifying women is not okay."
Last week, Lucy Flores said Mr Biden had placed two hands on her shoulders from behind, smelled her hair then planted "a big slow kiss on the back of my head" at a campaign event.
That was when she was running as the Democratic candidate for Nevada's lieutenant governor in 2014.
Mr Biden had flown in to support her bid and the incident is alleged to have happened as she prepared to go on stage.
Ms Flores, too, has said - in an interview with the Huffington Post - that such behaviour is "disqualifying" for a presidential run.
Her allegations first appeared on Friday in an article she wrote for The Cut magazine.
Nancy Pelosi, who leads Democrats in the House, made her views known to Politico.
"I don't think it's disqualifying," she said of his yet unannounced presidential bid.
But she added: "He has to understand in the world that we're in now that people's space is important to them, and what's important is how they receive it and not necessarily how you intended it."
"Join the straight-arm club," she said, suggesting that he keep to handshakes only.
"Just pretend you have a cold and I have a cold," Ms Pelosi added.
Senator Elizabeth Warren, a Democrat who has declared she will try for the nomination, said Mr Biden "needs to give an answer".
Another leading Democratic Party presidential contender, Senator Amy Klobuchar said that in politics "people raise issues and they have to address them".
Support for Mr Biden was voiced by Cynthia Hogan, a former aide to the vice-president, who told the New York Times that he "treated us with respect and insisted that others do the same".
An ally of Mr Biden told CNN the former vice-president was not reconsidering any run for the White House following the allegations but stressed he had yet to make a decision.
The former Delaware senator, who served as Barack Obama's vice-president from 2009 to 2017, is seen as a possible front-runner in the race for the Democratic nomination.
Asked about the new allegation, a spokesman for Mr Biden referred reporters to a statement issued on Sunday.
"In my many years on the campaign trail and in public life, I have offered countless handshakes, hugs, expressions of affection, support and comfort. And not once - never - did I believe I acted inappropriately," it read.
"But we have arrived at an important time when women feel they can and should relate their experiences, and men should pay attention. And I will," he added.
Mr Biden and President Obama were known for their close friendship, often seen playing golf and attending sports events together. Mr Biden even said that Mr Obama offered him financial help when his son was ill.
For his vice-president's birthday in 2017, Mr Obama posted a photo of the two of them on Twitter, writing that Mr Biden was his "brother and the best vice-president anybody could have".
On Monday, a spokesman for Mr Biden accused "right wing trolls" of presenting harmless images of the former vice-president interacting with women over the years as evidence of inappropriate touching.
Mr Biden has yet to jump into the race, but plenty have. So who else has a shot at becoming the next president?
Newer articles