Abdel Razek Mejaidie, the security adviser to Mahmoud Abbas, the Palestinian president, said: "The instructions are clear. Anyone violating the national agreement will be considered to be breaking the law."
An official said 13,000 Palestinian security officials were on the ground in Gaza to stop the rocket attacks.
"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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Referring to the ceasefire Ehud Olmert, the Israeli prime minister, said: "All of these things ultimately could lead to one thing - the opening of serious, real, open and direct negotiations between us ... so that we can move forward towards a comprehensive agreement between us and the Palestinians."
He said the truce could help revive long-term peace negotiations to resolve the conflict.
A deal could help ease pressure on Olmert following the Israeli military's failure to defeat the Lebanese Shia group, Hezbollah, during the summer conflict in Lebanon.
The ceasefire also comes at a time of growing US pressure on Israel and the Palestinians to end the ongoing violence.
George Bush, the US president, is due to visit the region next week.
The ceasefire went into effect at 6am (4:00 GMT) on Sunday.
"All of these things ultimately could lead to one thing - the opening of serious, real, open and direct negotiations between us"
Ehud Olmert, Israel's prime minister
Q & A on Gaza truce
Mahmoud Abbas had earlier told Olmert that he had arrived at an agreement with all Palestinian factions that rocket attacks from the Gaza Strip would 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The Israeli army said on Sunday morning it had withdrawn all forces from the Gaza Strip ahead of the ceasefire.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 had 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.