"All of these things ultimately could lead to one thing - the opening of serious, real, open and direct negotiations between us," Olmert said.
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"Everyone is included in this agreement... it is necessary to make all efforts to respect it"
Ghazi Hamid, Palestinian government spokesman
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"So that we can move forward towards a comprehensive agreement between us and the Palestinians."
The armed wing of the governing Hamas movement also earlier said it fired two rockets at Israeli targets, arguing Israeli troops were still inside Gaza despite a statement from the army that all had withdrawn.
Palestinian officials said that security forces would be deployed to stop fighters launching rockets from Gaza.
Amir Peretz, the defence minister, said Israel would press military operations if rockets continue to fall in the south.
Truce agreement
Ghazi Hamad, the Palestinian cabinet spokesman, said the government would speak to the factions which violated the truce.
"We will have to discuss any violation of this (ceasefire) agreement by Hamas, Fatah, Islamic Jihad, the Popular Front for the Liberation of Palestine or the Democratic Front for the Liberation of Palestine," Hamad said, according to Israel army radio.
"Everyone is included in this agreement which is signed by everyone, including by Islamic Jihad and it is necessary to make all efforts to respect it."
The ceasefire went into effect at 6 am (4:00 GMT) on Sunday.
Mahmoud Abbas, the Palestinian president had earlier told Ehud Olmert, the Israeli prime minister, that he has arrived at an agreement with all Palestinian factions that rocket attacks from the Gaza Strip will stop.
In Jerusalem, Miri Eisin, a spokeswoman for Olmert, said: "Abbas asked in response that Israel stop all military operations in the Gaza Strip and withdraw all the forces."
The Israeli army said on Sunday morning it had withdrawn all forces from the Gaza Strip ahead of the ceasefire.
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.
Fighters killed
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".