"Terror activity against innocent women and children is intolerable," Biden told former president Shimon Peres during their meeting.
Biden "condemned in the strongest possible terms the brutal attack which occurred in Jaffa," his office said. "He expressed his sorrow at the tragic loss of American life and offered his condolences to the family of the American citizen murdered in the attack, as well as his wishes for a full and quick recovery for the wounded," the statement said.
The American vice president stressed the United States' "absolute, total, unvarnished commitment to the security of Israel," saying he hopes progress can be made on the peace process and the fight against terror.
Biden and Peres were told of the stabbing attack that was happening not far from where they were, but Biden's visit and his meeting with Peres continued uninterrupted.
A 22-year-old Palestinian from Qalqilya rank amok along the Jaffa boardwalk, stabbing anyone in his path. He killed one person, said to be an American tourist, and wounded 11 others.
"There are serious terror attacks in Israel even today," Peres told Biden. "In these very moments, there is a terror attack in the nearby streets. Terrorists want to hurt innocent people and they want to hurt the State of Israel. We will not give up and will continue fighting terror with all our might."
"The majority of the people know there is no alternative to the two state solution ... and we shall follow with all our strength and dedication to make from it a new reality," Peres added.
"It is up to us, Israel and the United States together, to do everything we can in order to fight terror and bring an end to the bloodshed and war," Peres said in a statement released by his office.
After the meeting, Peres said: "I notified the Vice President on the terrible incident that took place just a few hundred meters away from here in Jaffa. He wanted to know every detail and the names of the families and how the wounded were doing. Throughout our entire meeting, we received updates on the attack and the condition of the wounded, and it was clear that there is no compromising when fighting terror - both in Israel and the US - and that terror will be defeated, despite all of the sorrow and pain."