In response to Friday's killing, Allah Sanakeh, a spokesman for the group, said al-Aqsa Martyrs Brigades would not honour a decree by Abbas that armed groups hand over their weapons.
Sanakeh said the Brigades needed to continue to respond to Israeli raids.
Abbas had said he would no longer permit Palestinians to bear illegal weapons, though it was not clear how he intended to implement the decision.
The Israeli raid signalled Tel Aviv would continue to pursue Fatah fighters despite its pledges to bolster Abbas as he tries to stabilise his hold in the West Bank after Hamas movement seized control of the Gaza Strip two weeks ago.
Salam Fayyad, the Palestinian prime minister, has accused Israel of trying to undermine Abbas's Western-backed emergency cabinet by conducting the raid despite the Palestinian leader's vow to take his own steps to disarm gunmen.
Fighting Israel launched the raid in the Nablus area on Thursday, sending in 50 armoured vehicles.
The Israeli army imposed a curfew on the city centre and searched houses for Palestinians suspected of involvement in violence against Israel.
In fighting on Thursday, Israel fired rubber coated steel bullets that injured seven Palestinians, and five Israeli soldiers were also wounded in the violence, Israeli and Palestinian security sources said.
Israel has also renewed raids against Hamas strongholds in Gaza.
Twelve Palestinians were killed in the raids, including a 12-year-old boy, in the coastal area on Wednesday.