The Palestinian Fatah movement says it will boycott all cabinet meetings of the coalition government with Hamas until a Gaza ceasefire is implemented.
Residents say fighting has been the worst for months
The move follows two days of factional fighting, which has left 34 dead.
In northern Gaza Hamas overran the headquarters of the Fatah-controlled National Security Forces.
Elsewhere, a mortar was fired at the compound of Palestinian leader Mahmoud Abbas, from Fatah, and a rocket hit the home of Hamas PM, Ismail Haniya.
Frustrated Egyptian mediators said the rival factions appeared uninterested in talks.
The head of the mediation team, Lt Col Burhan Hamad, said: "It seems they don't want to come. We must make them ashamed of themselves. They have killed all hope. They have killed the future."
Israeli Prime Minister Ehud Olmert on Tuesday expressed concern at the violence and said international forces should be stationed on the Egyptian border with Gaza to stop arms reaching militant groups.
Human Rights Watch accused Palestinian gunmen of war crimes and violations of international humanitarian law.
"Both Fatah and Hamas military forces have summarily executed captives, killed people not involved in hostilities, and engaged in gun battles ... inside and near Palestinian hospitals," the group said.
Radio stations and hospitals
Witnesses said Tuesday had been the worst fighting they had experienced in Gaza during 18 months of internal strife.
Hamas came out the dominant force in Tuesday's exchanges
"Since early morning we have heard explosions and shooting. We can't go and buy any food, we can't stand in front of the windows, all our children are in one bedroom," said Gaza City resident Adnan.
A major Fatah base in the northern town of Jabaliya fell to Hamas fighters, witnesses told AFP news agency.
Heavy fighting also raged around the main Fatah headquarters in Gaza City, with Hamas militants attacking with rocket-propelled grenades and automatic weapons.
Pro-Fatah security forces attacked Hamas's al-Aqsa TV and radio stations in Gaza, and reportedly took control of broadcasts - playing Fatah songs instead of the usual broadcasting schedule.
The under-secretary for transport, Saidi Tamimi of Hamas, was abducted by gunmen who stormed his office in Ramallah on the West Bank.
A cousin of Abdel Aziz Rantissi, a Hamas leader killed by Israeli forces in 2004, was reportedly kidnapped and killed by Fatah gunmen.
Mr Abbas accused some Hamas figures of "planning a coup against legitimate institutions". He urged an immediate ceasefire and talks to end the bloodletting.
The Fatah central committee held an emergency meeting on Tuesday, attended by Mr Abbas, and decided to suspend its unity government with Hamas until the clashes stopped.
"[Fatah] ministers will no longer participate in the government if the shooting does not stop," a statement said.
The BBC's Katya Adler in Ramallah says that in Gaza street corners, rooftops, even hospitals have become battlegrounds with most Gazans too scared to leave their homes.
In one incident, a senior member of the al-Aqsa Martyrs' Brigades, linked to Fatah, was shot 41 times while in a hospital bed in the town of Beit Hanoun.
A surgeon in Gaza's biggest hospital in Shifa, said that one man, injured in earlier fighting, was attacked even while he was being treated.
"While doctors were trying to save his life some of the masked people who are carrying his weapon came to the bed and he shot at him and then he died," Dr Jumaa Saqqa told the BBC.