The move on Saturday came hours after Abbas accepted the resignation of West Bank national security chief General Haj Ismail Jabir over the shooting incident which took place late on Wednesday inside the compound housing the Palestinian leader's headquarters.
The fighters were members of al-Aqsa Martyrs' Brigades, a group with ties to the ruling Fatah movement.
Hundreds of Palestinian security forces were on patrol in Ram Allah "to assure order and security" even though Israel has yet to officially transfer control in the city to the Palestinians.
Abbas also sacked Ram Allah security chief Yunis al-Has, in the wake of the shooting which has highlighted persistent lawlessness in the occupied territories, officials said.
In the wake of the shooting, West Bank intelligence chief Tawfik Tirawi handed in his resignation, but it was not immediately accepted by Abbas.
"He did this because of the corruption and the shooting against the president's office, which the security forces have done nothing about," an official said on Friday.
Meanwhile, in the southern West Bank town of Hebron, Jewish settlers took over a house belonging to two Palestinian brothers, Palestinian security sources said.
Israeli soldiers in the area did nothing to intervene as the settlers entered the two-storey house in the Tal Rumaida neighbourhood and threw all the contents into the street.
The two brothers fled their home over four years ago following repeated harassment by the settlers, they said.