The sanctions come the same day that similar measures were taken by the European Union Council, which sanctioned four individuals and two entities including Lehava.
The abuses include "torture and other cruel, inhuman or degrading treatment or punishment," the EU Council said in a statement.
There are conflicting reports from settlers, Palestinians, and the army as to the cause and nature of the brawl, as well as who shot the Palestinians.
The violence errupted after the murder of 14-year-old shepherd, Binyamin Achimair.
Shaul Golan, a photographer and journalist with Yediot Aharonot and Ynet, spoke of how he was beat by settlers in the West Bank, and much of his equipment destroyed.
For the EU to follow suit it would need consensus from all 27 of its member states.
The EU has not spelled out what the sanctions would entail but officials have said they would include bans on travel to the EU.
Biden told Netanyahu that the US intends to continue to act against settlers who are involved in attacks against Palestinians in the West Bank.
The sanctions follow the US imposition of travel visa bans in December on people involved in violence in the West Bank.
To justify this terror-rewarding move, there was a need to show the violence from Israel’s side, namely “settler violence.”