Heavy fighting has continued throughout the day in Gaza after militants of the Palestinian group Hamas attacked posts held by their Fatah faction rivals.
Fighting has taken on a new intensity and brutality in recent days
Hundreds of Hamas fighters had moved on the positions after giving their occupants two hours to leave.
Fatah leaders say they will no longer participate in the three-month-old unity government they formed with Hamas unless the fighting ends.
At least 34 people have been killed in Gaza over the past two days.
The residences of both Mahmoud Abbas, Fatah's leader and the Palestinian Authority president, and of Prime Minister Ismail Haniya, of Hamas, have been targeted with gun and shell fire.
Witnesses said it was the worst fighting they had experienced in Gaza during 18 months of internal strife.
"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.
Hamas began attacking Fatah posts after an 1100 GMT deadline for fighters to leave expired.
A major Fatah base in the northern town of Jabaliya fell to Hamas fighters, witnesses told AFP news agency.
Few places are considered safe in the strife-torn streets of Gaza City
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.
'No interest in talks'
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.
The International Committee of the Red Cross said it was "deeply disturbed by the events in Gaza over the last two days, particularly the attacks in and around two hospitals in the northern part of the Gaza Strip".
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.