Members of Fatah's al-Aqsa Martyrs Brigades, the armed men exchanged fire with police in Gaza City on Wednesday in an attempt to shut an election office.
Staff took cover inside before police drove the men off.
Elsewhere, Brigades fighters forced two offices to close.
The armed men demand changes to the latest proposed list of election candidates, which was due to be submitted by Abbas on Wednesday as a way to patch up a damaging split between Fatah veterans and younger rivals.
Members of the al-Aqsa Martyrs' Brigades have threatened to shut election offices across Gaza and the West Bank, possibly preventing Abbas, the Palestine president, from submitting Fatah's latest list of candidates for the 25 January parliament ballot.
Divisions in Fatah between veteran leaders, a young guard seeking a bigger share of power and resistance fighters waging a five-year-old uprising (intifadah) against Israel, have boosted Hamas before the election.
At Fatah's request, election offices were to re-open for several hours on Wednesday so that Abbas could submit a new list of candidates, bringing together members of rival wings who had earlier submitted separate lists.
But al-Aqsa Martyrs Brigades fighters said they were protesting because they were not properly represented on the new list - which has still not been finalised.
About 30 Brigades fighters forced the election office in the southern Gaza Strip city of Khan Yunus to close.
In nearby Rafah, election officials walked off the job after the armed men appeared despite appeals from police.
Mahmoud Abbas was to submit
a new list of election candidates
Abu Zakariya, leader of the group in Khan Yunus, said: "Our voices have been lost."
The men demanded a re-run of a primary election to choose Fatah candidates and, if need be, a postponement of the ballot.
A senior official of the elections commission said in the West Bank city of Ram Allah that there had been no formal decision to close the Gaza offices despite the presence of the armed men.
He said the doors were shut and workers had gone home.
Fatah fighters also seized election offices briefly in the West Bank on Tuesday.
The growing crisis within Fatah in the run-up to the vote has encouraged some Palestinian officials to push Abbas for a postponement.
But Hamas, contesting for the first time, rejects any delay.
The group is seen by many Palestinians as less tainted by corruption than Fatah.