Two Fatah members shot dead as armed rivals continue to roam the streets.
An Israeli army spokeswoman said “three rockets were identified being fired from the northern Gaza Strip”, and they caused no damage or casualties.
If Israel retaliates, that would only add to the woes of ordinary Palestinians, who are frustrated by the surge in factional tensions and pessimistic about a lasting truce between Fatah and Hamas.
“There will be a comprehensive ceasefire in Gaza to end all military demonstrations, all shooting will stop and random deployments will end.”
A previous ceasefire broke down within 24 hours and it is unclear whether this one, scheduled to take effect at 11pm (2100 GMT), will hold.
“We bless and support this agreement. After one hour, it will take effect.”
Fighting had continued in Gaza during the day on Wednesday and there was little evidence to suggest that Hamas or Fatah forces had begun to withdraw from the streets.
One Fatah spokesman, Tawfiq Abu Khoussa, said: “Unless Hamas stops its violations, the second agreement … could be in danger.”
Palestinian sources said they expected Abbas to hold a long-awaited meeting with Olmert in the next few days.
While such a meeting would be seen as a possible spur to reviving peace talks between Israel and Abbas, Olmert has said the Palestinians could expect little until a soldier held captive in Gaza since June was freed.
Olmert refuses to negotiate with Hamas, the faction that was elected into power in January.
Israel now says it is considering handing over $500 million in withheld Palestinian tax funds to Abbas in a move that could bolster him in the run-up to early elections.
This move would allow Abbas to make direct payments to Palestinian civil servants, who have not received their full salaries since Hamas came to power.
Israel has been under pressure from Europe and the UN for months to release the tax money to Abbas, who favours peace talks with Israel.
However, Israel wants assurances that the money will not benefit Hamas or its government, sources said.
Fawzi Barhoum, a Hamas spokesman, said the ruling faction would prefer the tax money to go through the Hamas-led government.
“We have no objection as long as its final destination will be the employees and our needy people”
Fawzi Barhoum, Hamas spokesperson
“But under the current siege, if this money comes through any other channel, including the channel of the president, we have no objection as long as its final destination will be the employees and our needy people,” he said.
A senior aide to Abbas said the president planned to issue a decree next week to lay the legal foundations for elections, which Hamas says are unconstitutional.
Abbas said on Wednesday that he was “not opposed” to restarting talks with the ruling Hamas movement on forming a coalition government, despite his call for early elections.
Western diplomats said earlier this week Western powers and their Arab allies would try to boost Abbas before the elections, but Palestinian analysts said the effort could backfire if Hamas succeeded in painting Abbas and Fatah as beholden to US and Israeli interests.
Condoleezza Rice, the US secretary of state, had said on Friday she would ask the US Congress for tens of millions of dollars to strengthen the Fatah security forces.