There was no claim of responsibility for the incident which took place at a checkpoint, but Fatah officials blamed Hamas for the killing.
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Eight people were also wounded in gun battles.
At least 24 Palestinians have been killed and more than 200 wounded since Hamas fighters ambushed a convoy they said was carrying military equipment to Abbas's forces on Thursday.
Gaza residents said they expected to find out by daybreak whether the ceasefire, announced by Saeed Seyam, the Hamas interior minister, after talks with a top Fatah security official, had any chance of taking hold.
The conflict has brought Gaza to a near-standstill and increased pressure on the Quartet of peace brokers - the US, the UN, European Union and Russia - to make a fresh effort to revive Middle East peace talks.
Seyam said he and Rashid Abu Shbak of Fatah agreed on "an immediate ceasefire, removing gunmen from the streets and rooftops of buildings and removing all the checkpoints".
Police would also be deployed to restore law and order on the streets, he said, replacing rival security forces which were facing off across Gaza, home to 1.5 million Palestinians.
Hamas, the Palestinian Islamic resistance movement, took control of the Palestinian government last March after beating Abbas's secular Fatah group in parliamentary elections.
At the urging of Saudi Arabia's King Abdullah bin Abdulaziz, Abbas and Hamas's political leader Khaled Meshaal agreed to hold meetings on Tuesday in the city of Mecca to try to resolve their differences over a unity government, Nabil Abu Rdainah, an Abbas aide, said.
|Palestinians in the West Bank pray in Nablus|
for a quick end to the strife in Gaza [AFP]
On Saturday, Hosni Mubarak, the Egyptian president, said the Palestinians were close to agreeing a government, but gave no details.
"It is about to be finalised unless a surprise happens," he said in Cairo in the presence of visiting German Chancellor Angela Merkel.
Residents in Gaza, however, remained wary.
More than 80 Palestinians have been killed in fighting since talks on a Palestinian unity government broke down in December and Abbas called for early elections, a step the governing Hamas movement condemned as a coup.
Hamas accuses Washington of fuelling the fighting to bring down the government.
The US has pledged $86m to bolster thousands of Abbas's security forces.
Documents obtained by Reuters show the assistance programme could cover at least 13,500 troops loyal to Abbas.