A second woman has come forward, claiming former Vice President Joe Biden touched her inappropriately at a political event. Former congressional aide Amy Lappos told the Hartford Courant that Biden reached for her face and rubbed noses with her during a 2009 fundraiser in Greenwich, Connecticut.

In a statement to CBS News, Lappos said Biden should not run for president and that "objectifying women is not okay."

"Men who invade a woman's personal space, touch women inappropriately, sexually harass women and feed rape culture have no place in a position of power. Referring to this type of behavior as 'simply affection' or 'grandpa-like' or "friendly' is ridiculously dismissive and part of the problem," the statement said.

"If Biden truly supports women and gender equality he would step aside and support one of the many talented and qualified women running. The same goes for the other men who have thrown their hat in the ring."

On Friday, former Nevada assemblywoman Lucy Flores recalled a 2014 campaign event where Biden approached her from behind, smelled her hair and kissed her head. "This isn't new. I'm not bringing up something that people have not been aware of," Flores said.

She said Biden's behavior wasn't sexual, but should be a factor in the Democratic primary. Yet, were he to win the nomination and square-off against President Trump, she said "that's not even a question."

"Of course I would support Biden," she said.

In a statement, Biden said over the years, "I have offered countless handshakes, hugs, expressions of affection, support and comfort. And not once — never — did I believe I acted inappropriately. 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."

Several women came to Biden's defense on Monday, including Stephanie Carter, seen with Biden at the swearing-in of her husband, former Secretary of Defense Ash Carter. She said that moment has been misinterpreted, that he was "helping someone get through a big day, for which I will always be grateful."

At a forum for already-announced candidates in Washington, some said it will be up to Biden to decide whether to run for president and for voters to judge his behavior.

People in the crowd at that event were split. Some hadn't heard about it. If he runs, Biden isn't expected to jump in to the race until later this month at the earliest.