In a meeting held in the West Bank city of Ramallah, the PLO executive also recommended that Abbas declare a state of emergency in Gaza and the West Bank, and seek international protection against Izz al-Din al-Qassam Brigades, Hamas's armed wing.
"The executive committee authorised Abbas to take whatever decision he judges appropriate with regard to the government and to resolve the current crisis," said one participant.
More than 80 people have been killed since Saturday in the worst factional violence since Hamas won a parliamentary election last year.
In the centre of Gaza City on Thursday, Hamas fighters seized control of a security compound after the expiry of a deadline for its occupants to surrender.
Hamas's trademark green flags were later observed fluttering from the rooftop of the heavily fortified Preventive Security headquarters.
An intelligence compound in Gaza City was taken hours later.
A bomb ripped through a Gaza studio of the official Voice of Palestine radio which is close to Fatah, forcing the station to stop broadcasting, witnesses said.
Nour Odeh, Al Jazeera's correspondent in Gaza, said there were reports of Hamas celebratory gunfire at the Preventative Security headquarters.
"A number of Hamas leaders had been detained by the Preventative Security forces in previous years and this had compounded Hamas fighters' hatred towards those forces," she said.
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
Sami Abu Zuhri, a spokesman for Hamas, said the capture of the headquarters marked its liberation.
"It was liberated from the herds of collaborators," he said, referring to Fatah, which has pursued peace negotiations with Israel.
Hamas has also captured a compound housing security services in the southern Gaza Strip town of Rafah, a statement from Izz al-Din al-Qassam Brigades said.
Witnesses confirmed that Hamas had taken the compound, which houses the local headquarters of national security, Palestinian intelligence, police and preventive security.
Also in Rafah, five children were killed by an Israeli tank shell, according to medical staff in the town. The Israeli army denied any knowledge of the incident.
West Bank violence
In the West Bank, armed men loyal to Fatah retaliated against Hamas, shooting and wounding a Hamas supporter near Ramallah and seizing Hamas loyalists in Jenin and Nablus.
Jacky Rowland, Al Jazeera's correspondent in Ramallah, said Fatah supporters were targeting Hamas opponents.
"We've been seeing Fatah gunmen, many of them al-Aqsa gunmen from the Fatah military wing, targeting business and schools affiliated to Hamas and even the homes of individuals," she said.
"In particular… a statement by al-Aqsa Martyrs Brigades says they consider they have the full authority to capture members of Hamas."
The European Commission has meanwhile suspended humanitarian aid to Gaza because of the factional fighting.
"The humanitarian situation is catastrophic, we have had to withdraw our [aid] operators," said Louis Michel, European Aid and Development commissioner.
|Hamas fighters have taken control of nearly|
all major political offices in Gaza [AFP]
Last year, the EU executive provided $111.7m of humanitarian aid to the Palestinian territories.
The European Commission said the aid will only resume if fighting ceases.
Hamas officials have said Ismail Haniya, the Palestinian prime minister, wants full control of Palestinian security forces under the terms of an agreement sealed in Mecca, Saudi Arabia, in March.
Fatah said on Tuesday that it may abandon the unity government, which could let Abbas rule by decree, despite his limited authority in Gaza.
Analysts say a Fatah break with Hamas could divide the West Bank and Gaza Strip, the two territories Palestinians want for their state.