Mahmoud Abbas, the president, said that the violence was part of a Hamas-led coup attempt.
After the closed-doors meeting, Fatah's central committee said in a statement: "The committee has decided that [Fatah] ministers will no longer participate in the government if the shooting does not stop."
Ismail Haniya, the prime minister and Hamas member, said a state of emergency should be declared and that talks between the two factions should resume.
In Israel, Ehud Olmert, the Israeli prime minister, said an international force should be deployed along the Gaza-Egypt border.
Abbas's office said in a statement: "All information and events on the ground in Gaza confirm that there is a group in the Hamas movement, including political and military leaders, that are planning to carry out a coup against the Palestinian legitimacy.
"The Palestinian presidency is worried about this plot ... which is pushing the homeland into an ugly civil war."
Nour Odeh, Al Jazeera's correspondent in Gaza, said: "For the president to make such a declaration does signal a new chapter in this Hamas-Fatah violence.
"The situation does not seem to be reaching a solution, it seems to be heading further and further away from political dialogue."
Haniya's home struck
A rocket-propelled grenade was fired into the Palestinian prime minister's house on Tuesday morning. Haniya, who is a member of the Hamas movement, was unharmed.
Izz al-Din al-Qassam Brigades:
- Armed wing of Hamas
- Estimated 15,000 members
- Security force set up by Hamas in 2006
- Estimated 6,000 personnel
- Mainly drawn from armed wing of Hamas
- Majority loyal to Fatah
- Up to 5,000 personnel
- Best equipped and trained security force
- US gave $43m to help restructure force
National Security Forces:
- Under direct command of president
- Includes military intelligence, naval police and Elite Force 17
- Up to 30,000 personnel
Police and Preventive Security:
- Under Hamas-led interior ministry
- Dominated by Fatah loyalists
- Estimated 30,000 personnel
Al-Aqsa Martyrs Brigades:
- Offshoot of Fatah faction
- Several thousand members
- Many work for the security services
Fawzi Barhoum, a Hamas spokesman, accused Fatah of firing the rocket in an attempt to assassinate Haniya and vowed punishment "without mercy" of the perpetrators.
"Hamas has decided to punish the attackers and the killers and it will not be reluctant to punish them without any mercy."
It was the second time since Monday that Haniya had come under attack, a shooting at his office on Monday interrupted a cabinet meeting but caused no casualties.
Later, an aide to Haniya said that Hamas's rivals were trying to bring down the unity government which was formed in March.
"Certain parties, collaborating with parties hostile to our people, have tried to bring down the government of national unity by force," the official said.
Witnesses said that a large security compound in Gaza City was attacked just minutes after the Hamas deadline expired. Heavy gunfire and explosions were heard in the area, but there was no immediate word on casualties.
A second headquarters in Jabiliya, in the north of the strip, was also besieged.
Hamas-affiliated radio stations said fighters had taken control of security installations in northern and central Gaza, as well as the southern town of Khan Yunis.
Earlier, the presidential compound in Gaza City also came under attack with mortar shells, an officer in Abbas's presidential guard said.
|At least 18 people have been killed since |
the fighting escalated on Monday [EPA]
A gun battle broke out between armed supporters of Hamas and Fatah at a hospital in Khan Yunis.
Hamas fighters reportedly controlled the roof of the European Hospital and Fatah-allied fighters took up positions nearby.
"[Medical officials] are appealing to gunmen from all sides to steer away from medical services, institutions and ambulances and allow them to do their work," Odeh said.
The recent clashes have been particularly brutal with reports of fighters dropping rivals to their deaths from high-rise buildings and bodies being mutilated.
Officials of both factions have seen their homes attacked and in many cases set on fire.
'House for a house'
Samih al-Madhoun, a senior figure in the Fatah-linked al-Aqsa Martyrs Brigades, said after his house was attacked: "If they've burnt my house, I have burnt 20 Hamas houses last night."
"A house for a house and blood for blood ... I swear to God that I will kill every member of Hamas, be they civilian or military. I will kill them all," he told a Fatah radio station.
The factional fighting spread to the West Bank as Saidi Tamimi, deputy transport minister and a Hamas member, was seized by armed men who stormed into his department and forced him into a vehicle, security officials said.
Also in Ramallah, presidential guards stormed Hamas-controlled al-Aqsa Television and seized equipment. Three staff were detained, the station said.
The raid came after two television employees were abducted and their station set on fire overnight. Palestine TV blamed Hamas for the raid.
Fighters also renewed rocket attacks on southern Israel. Three Israelis in the town of Sderot were lightly injured, an Israeli medic said.
Israel launched an air strike into the northern Gaza Strip after the Islamic Jihad group claimed responsibility for the attack.