The internal conflict erupted on Thursday night and resumed on Friday after fighters fired rockets into southern Israel, killing a young woman, and Palestinian police then confronted them in an effort to prevent further barrages.
"One civilian was killed and a total of 16 injured, several of them seriously," a doctor at a Gaza hospital said.
One of the dead was named as Ismail al-Amarin. Doctors later pronounced a second civilian dead, saying he too had been shot in the head. Witnesses said the two dead were unarmed male teenagers.
Fighting raged in the Zaitun neighbourhood of Gaza, a known Hamas stronghold, pitting Palestinian security forces in armoured vehicles against resistance fighters firing anti-tank missiles, witnesses said.
Hospital sources said six of the wounded were members of the security forces and the rest were civilians, some of whom were caught in the crossfire in the densely populated neighbourhood.
By midday Aljazeera reported that Islamic Jihad had offered to mediate between Hamas and the police, calling for a ceasefire between the sides and an urgent meeting to resolve the differences.
In a statement, the resistance movement rejected the use of force between Palestinians, stressing that all arms should be directed to the Israeli enemy.
Shooting in hospital
Families of the casualties were outraged by the violence and armed relatives fired shots inside Shifa hospital before Palestinian police moved in to restore order.
In the wake of a salvo of rocket attacks, Palestinian interior minister Nasr Yussef ordered security forces and police to "prevent by force if necessary all firing of rockets and mortars" against Israeli targets.
The fighting was the worst among Palestinians since the mid-1990s when Palestinian police killed more than a dozen protesters in clashes with stone-throwers outside a Hamas-stronghold mosque.
Abbas is trying to preserve a
shaky ceasefire with Israel
The Palestinian interior ministry blamed Hamas for firing on Palestinian police.
But in an interview with Aljazeera, Saeed Siam, a senior Hamas leader denied Hamas' role in the allegations.
Minister should go
Hamas spokesman Sami Abu Zuhri demanded the sacking of the Palestinian Interior Minister Nasr Yousef, blaming him for the security deterioration and escalation of clashes in the Gaza Strip between Hamas and Palestinian security.
Abu Zuhri told Aljazeera the clashes were not spontaneous but were a deliberate attempt by the Palestinian Authority to prevent Hamas from "defending the Palestinian people against Israel aggression".
He said Palestinian security forces have clear instructions to use force, including open fire, to block any attempt to fire missiles against Israel.
"The Palestinian Authority should seek to protect the Palestinian people, not the Israeli settlements," he said.
Abu Zuhri (R) has called for the
sacking of Nasr Yousef
However, he affirmed that Hamas remained committed to the truce, but the truce must be respected by the both sides.
Hamas could not remain inactive in the face of repeated and continued Israeli aggression, he added.
Palestinian President Mahmoud Abbas, struggling to preserve a shaky ceasefire with Israel, had ordered his security forces to silence the rockets as Israel vowed to act on its own to stop the latest attacks.
Fighters said the rocket attack avenged the killing of a comrade in an Israeli raid in the West Bank on Thursday; part of an Israeli offensive against Islamic Jihad fighters after one of them killed five Israelis in a bombing.