The political leader of Hamas says Palestinians could begin a new uprising.
He said Abbas had phoned Olmert and that the Israeli prime minister had “agreed that Israel will stop operations and begin the withdrawal from Gaza at the same time”.
In Jerusalem, Miri Eisin, a spokeswoman for Olmert, said: “Abbas told the prime minister that all the Palestinian factions are committed to the agreement.
“Abbas asked in response that Israel stop all military operations in the Gaza Strip and withdraw all the forces.
“The prime minister… told Abbas that Israel would respond favourably as Israel was operating in the Gaza Strip in response to the violence. With the end of violence Israel would be happy to withdraw its troops.”
The truce announcement held out the promise of a possible resumption of long-stalled peace talks.
Palestinian fighters have been firing rockets into southern Israel daily in what they say is a response to Israeli attacks in the Gaza Strip.
Israel withdrew troops from the territory last year but resumed ground operations there in June after fighters from Gaza tunnelled across the border and captured an Israeli soldier, who is still being held.
On Saturday the Israeli army killed three Palestinians, including a fighter from the armed wing of Hamas, in an air strike on his minibus, medics and witnesses in Gaza City said.
Four other members of the Ezzedine al-Qassam Brigades were wounded in the missile attack on their vehicle in the city’s eastern Zeitun district.
An Israeli army spokeswoman said it had targeted Hamas members “involved in firing rockets at Israel”.
Earlier on Saturday, Israeli soldiers clashed with Palestinian fighters in the northern Gaza Strip, killing one of them, local hospital officials said.
In a separate incident overnight on Friday, an unidentified Palestinian was shot dead by Israeli troops while approaching the strategic Karni border crossing.
Afterwards, Israeli tank shells hit a house and a car in the same part of Gaza, causing at least two injuries, hospital officials said.
Israeli tanks and troops have been operating in the area east of Jabaliya. The explosions took place shortly after fighters fired rockets into Israel, residents said.
An army spokeswoman said the tank shells were fired at the rocket launchers.
Two fighters escaped from the car with minor injuries. It was not immediately clear whether anyone was inside the house.