At least seven people were injured on Wednesday in the shootout with bodyguards after the attacks on the home of preventive security chief Rashid Abu Shbak, and the head of Fatah in Gaza, Abd Allah Franji, security and Hamas sources said.
While the security sources accused members of Hamas' armed wing, the Izz al-Din al-Qassam Brigades, of initiating the latest violence, Hamas said the shooting had been started by the security services.
Hamas spokesman Sami Abu Zuhri said members of the preventive security services had opened fire on a car containing members of Hamas as they drove past Abu Shbak's house, and that one of Franji's bodyguards also shot at a Hamas vehicle.
Abu Zuhri said four members of Hamas were wounded in the exchanges, while hospital sources confirmed that three members of the security services had also been injured.
Both attacks happened around dawn in Tal al-Hawa neighbourhood in southern Gaza City.
Tuesday's violence was centred
in Bait Lahya and Jabalya
Several hours earlier, Fatah and Hamas officials had announced they had reached an agreement to end factional violence.
Further talks between the factions were expected to take place later in the day in Gaza City to consolidate the truce, sources on both sides said.
At least 22 people were wounded on Tuesday during clashes in the northern Gaza Strip between Hamas and members of either the security services or Fatah.
Those clashes had been confined to the Jabalya and Bait Lahya areas, which lie to the east of Gaza City.
There were no reports of fresh fighting in either area early on Wednesday.
Abu Zuhri said that despite the fresh clashes in Gaza City, all sides were keen to draw a line under the violence.
Al-Zahar says there is a lack of
trust between Hamas and the PA
"There is a desire among our movement and the leaders of the Palestinian Authority (PA) to put an end to this issue and to implement this 'quiet' on the ground," he said.
Hundreds of people demonstrated outside the Palestinian parliament in the West Bank town of Ram Allah on Tuesday to call for national unity and an end to the security chaos in the occupied Palestinian territories.
The long-running rivalry between Fatah and Hamas has been stoked recently by the movement's refusal to accept an offer to join a national unity government.
The head of Hamas in its Gaza stronghold, Mahmud al-Zahar, said in a recent interview that there had been a permanent breakdown of trust between his organisation and the PA.
But Abu Zuhri told Aljazeera that Hamas and Fatah had agreed to improve relations to contain the current crisis.
"We do not want to go backward. We have achieved good progress to end this crisis and we will do our best efforts to end it completely"
Sami Abu Zuhri,
"Hamas contacted Fatah movement overnight. We hope we can announce on Wednesday a final end of this conflict," he said.
"We do not want to go backwards. We have achieved good progress to end this crisis and we will do our best efforts to end it completely on Wednesday," Abu Zuhri said.
"We, at Hamas, are interested in ending such incidents. We are sure we can end this crisis completely."
Also on Wednesday, Israeli occupation forces arrested seven protesters - mostly foreign - and Israeli activists during a peaceful protest against building the separation wall in Bilain village, west of Ram Allah.
Groups of protesters staged a sit-in in a water pipe in the confiscated lands, and wrote "let's free the land before we agree on who runs it" on the pipe.
Israeli soldiers attacked the protesters and announced the lands as closed military areas.