In Khan Yunis, the headquarters of the Preventive Security Force has reportedly been "totally destroyed" after a bomb exploded in a tunnel underneath it.
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"There are dead and wounded," Yussef Eissa, the Preventive Force chief, said as he blamed Hamas for the explosion. Hamas has not yet responded to the allegations.
Witnesses said that Hamas fighters had warned the officers inside the building to come out or they would blow the building up.
Hamas has taken over several posts from Abbas's National Security Force in the fighting, including a base in the northern Gaza Strip they captured after a bloody battle on Tuesday.
Residents reported that green Hamas flags were also flying from several smaller compounds in central Gaza. 'Bloody fighting'
Mortars and rockets were fired into the headquarters of the intelligence services in western Gaza City, facing stiff resistance from the men holed up inside, witnesses and security sources said.
"Bloody fighting has been going on since sunrise, numerous armed men have been killed. Their bodies are lying in pools of blood," Hossam Okal, who lives nearby, 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
Hamas fighters have also reportedly taken control of the coastal strip's main north-south road, putting them in position to cut off reinforcements to the security forces.
More than 60 Palestinians are estimated to have died since the fighting resumed four days ago.
The UN Relief and Works Agency (UNRWA) has suspended most of its operations in the Gaza Strip after two Palestinian employees were shot dead.
Christopher Gunness, UNRWA spokesman, said they appeared to have been caught in the crossfire rather targeted directly.
"In view of increased threats to our staff, UNRWA has no choice but to scale back its operations in Gaza with immediate effect," he said.
The agency has temporarily suspended all but emergency medical and food programmes.
About 1,000 Palestinians marched through Gaza City urging the rival factions to "stop the killing".
The demonstration drew gunfire from armed men on nearby buildings killing at least one protester. It was not immediately clear who was responsible for the shooting.
Nour Odeh, Al Jazeera's correspondent in Gaza, said some of the protesters fought with members of the rivals factions on the street.
Abbas said on Wednesday that the situation in the Gaza Strip was "madness".
"Without a stop to fighting, I believe that the situation will collapse in Gaza," he said. West Bank violence
The fighting spilled over into the previously calm West Bank on Wednesday as dozens of armed men loyal to Fatah stormed into a building in Nablus used by a pro-Hamas media company.
|Al-Aqsa Martyrs Brigades members|
seized Hamas supporters [Reuters]
Walid Batrawi, Al Jazeera's correpondent in the West Bank, said at least 15 people working in the office were abducted and taken to a nearby refugee camp.
"This is an escalation that is alarming in the West Bank if it spreads to other areas," he said.
Earlier Palestinian organisations and individuals staged a sit-in protest in Ramallah against the violence in the Gaza Strip.
"They were calling for national unity and blaming both the Palestinian government and the presidency for what is going on," Batrawi said.
Fatah's leaders said on Tuesday they would quit the three-month-old unity government they joined under Ismail Haniya, the prime minister and a Hamas leader, if the fighting did not end.
Both factions have accused others of escalating the violence and planning the fall of the Palestinian government.