The Israeli raid has signalled that Tel Aviv is prepared to continue to pursue fighters linked to Fatah, despite its pledges to bolster Abbas as he tries to consolidate his hold in the West Bank.
In a previous raid in June, Salam Fayyad, the Palestinian prime minister, accused Israel of trying to undermine Abbas's Western-backed emergency cabinet despite the Palestinian leader's vow to take his own steps to disarm fighters.
Meanwhile, a Hamas-led security force has said that it found a bomb outside the parliament building in the Gaza Strip.
Islam Shahwan, a spokesman for Hamas' Executive Force said: "We have thwarted a bombing attack against the parliament headquarters."
He said the bomb contained 15kg of explosives and was placed at the gate of the parliamentary compound.
"The engineering unit of the Executive Force defused the device. The Executive force is searching for the perpetrators."
There was no immediate claim of responsibility.
However, Fatah has been blamed.
"We think that several guys from Fatah are involved because this bomb is the same type as seven others that have exploded near Executive Force forces recently," Shahwan said.
Hamas took control of the Gaza Strip after fighting against Fatah three months ago.
However, violence has erupted between the two groups in recent weeks during a series of open-air prayer meetings organised by Fatah which had been banned by Hamas.