Fatah has reportedly postponed unity government talks with Hamas after at least 12 people were killed and 24 others abducted in factional violence across the Palestinian Territories.
The clashes on Friday overshadowed celebrations to mark the first anniversary of Hamas's election victory.
They also came after Mahmoud Abbas, the Palestinian president, said a deal could be done in weeks.
"The entire dialogue could explode," Tawfiq Abu Khoussa, the Fatah spokesman, said as he blamed Hamas for the violence.
"How can dialogue go on when there is a bomb underneath the table?"
The talks, which had been due to resume on Friday, will now be held on Sunday at the earliest.
Fighters from the Fatah-linked Al-Aqsa Martyrs Brigades captured 24 Hamas supporters and threatened a "severe response" if a senior activist whose home was besieged by Hamas security forces was harmed.
Mansour Shalayel's house in Jabalya, northern Gaza Strip, had been surrounded after he was blamed for the shooting of a Hamas supporter earlier on Friday.
Officials from the two factions reached a deal for an end to the siege and the release of the hostages late on Friday.
Residents said gunfire continued across the Gaza Strip late on Friday and Hamas and Fatah forces were deployed on the streets. Two rocket-propelled grenades were fired at Fatah's Preventive Security headquarters in Gaza City.
Hamas's celebrations to mark its victory over Fatah in parliamentary elections last January were scaled down due to the violence.
Hamas had originally said that the main rally would take place in Gaza City, but it was relocated to Jabalya after an attack on Hamas supporters on Thursday night and turnout was significantly less than expected.
Ismail Haniya, the Palestinian prime minister, pulled out of a planned appearance at the rally due to safety concerns.
Nour Odeh, Al Jazeera's correspondent in Gaza, said: "The showing was minimal, far below Hamas's expectation, because of what was going on on the ground."
About 40 Palestinians have been killed in fighting between the rival groups since Abbas called last month for presidential and parliamentary elections.
Abbas and Khaled Meshaal, the leader of Hamas, pledged on Sunday to curb Palestinian bloodshed after inconclusive talks to form a coalition government, which it is hoped may lead to the lifting of an international boycott imposed because of Hamas's refusal to recognise Israel, renounce violence and abide by interim peace deals.
The Hamas government has also been crippled by Israel withholding Palestinian tax revenues amounting to over $ 500m.
Abbas, speaking at the World Economic Forum in Davos, Switzerland, on Friday said: "We are at a junction now, either yes or no. I would tell you, this doesn't need more than two weeks, maximum three weeks.
"If we fail to achieve a national unity government that allows us to lift the siege, I will call for presidential elections."
Hamas has said any snap polls would be considered a coup.
In a statement issued before the Friday's rally, Hamas acknowledged difficulties in the year since its election triumph.
"Many of the programmes and the goals which the government has started to implement have been hit and obstructed by the outside siege ... and deprived our people of their salaries and food," it said.
In a veiled attack on Abbas, it also criticised "attempts by internal forces to make the government fail".
It said that formation of a unity government remained a "top priority", but it would not abandon "the rights of our people, especially the right of return and the right of resistance".
Source: AlJazeera and Agencies
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