Nearly 3,000 people died in those attacks, when Al-Qada hijackers flew planes against the World Trade Center towers in New York and the Pentagon in Arlington, Virginia, while a fourth plane crashed in Pennsylvania.
Passengers on United Airlines Flight 93 defeated the hijackers and the plane crashed into a field, preventing another target from being hit.
Mr Biden also met with members of the Association of Flight Attendants-CWA at the memorial, hugging some of them.