The executive also recommended that the president 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.
At what point will Palestinians stop playing the 'occupation' card and start taking responsibility for their own actions?
Roger, Detroit, US
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In the centre of Gaza City on Thursday, Hamas fighters fired mortars at a Fatah compound after the expiry of a deadline to surrender, which had earlier been broadcast on a Hamas radio station.
Hamas's trademark green flags were later observed fluttering from the rooftop of the heavily fortified Preventive Security headquarters.
Nour Odeh, Al Jazeera's correspondent in Gaza, said there were witness reports of Hamas celebratory gunfire at the headquarters.
"A number of Hamas leaders have been detained by the Preventative Security forces in previous years and this had compounded Hamas fighters' hatred toward those forces," she said.
"This means that Hamas has taken over the first headquarters of the Palestinian Authority security [but] there are at least two compounds – including the presidential compound – that remain in the hands of the Palestinian Authority."
Sami Abu Zuhri, a spokesman for Hamas, said the capture of the headquarters marked its liberation.
"It was liberated from the herds of the collaborators," he said, referring to Fatah, which has pursued peace negotiations with Israel.
Hamas also captured a security 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.
The European Commission has suspended humanitarian aid to Gaza because of the factional fighting.
|Hamas fighters have taken control of nearly|
all major political offices in Gaza [AFP]
"The humanitarian situation is catastrophic, we have had to withdraw our (aid) operators," said Louis Michel, European Aid and Development commissioner.
Last year, the EU executive provided $111.7m of humanitarian aid to the Palestinian territories.
Abbas spoke to Ismail Haniya, Palestinian prime minister and Hamas' main leader in Gaza, by telephone late on Wednesday.
Hamas officials said Haniya wants full control of Palestinian security forces under the terms of an agreement forged in Mecca, Saudi Arabia, in March.
The Mecca agreement led to Haniya bringing members of Fatah into a unity cabinet.
Abbas, officials said, has insisted that Hamas must stop fighting before he will negotiate.
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.