Israeli Prime Minister Ehud Olmert said the deal could help revive peacemaking that collapsed six years ago before a Palestinian uprising began.
For his part, Palestinian President Mahmoud Abbas, a moderate, instructed security chiefs to ensure the truce held.
The immediate aim is to end rocket fire from Gaza and halt a crushing Israeli army offensive launched after gunmen seized a soldier in a cross-border raid last June. Olmert said he hoped the soldier would now be freed.
‘‘All of these things ultimately could lead to one thing — the opening of serious, real, open and direct negotiations between us,’’ Olmert said.
‘‘So that we can move forward toward a comprehensive agreement between us and the Palestinians.’’
Militants launched at least nine rockets just hours after the start of the ceasefire.
‘‘We will show the necessary restraint and patience,” Olmert said in southern Israel.
The Israeli army pulled forces out of Gaza overnight and Palestinian witnesses confirmed the soldiers had gone.
There was little sign a truce was on the cards before it was announced late on Saturday. It came at a time of growing US pressure on Olmert and the Palestinians to curtail spiralling violence and show progress toward ending decades of conflict.
President Bush visits the region this week.
A deal could ease domestic pressure on Olmert after war in Lebanon and help end months of Palestinian political deadlock.
Islamic Jihad claimed responsibility for launching at least five rockets into southern Israel on Sunday. Hamas’s own armed wing and al-Aqsa Martyrs Brigades, part of Abbas’s Fatah, also said they had launched rockets.
More than 400 Palestinians, about half of them militants, have been killed in the offensive, Palestinian hospital officials and residents say. Three Israeli soldiers and two civilians have been killed since the assault began.
The ceasefire could pave the way for a summit between Abbas and Olmert on ways to restart peacemaking.
A halt to rocket attacks could also reduce pressure on Olmert at home, where his popularity has flagged after a July-August war against Hezbollah guerrillas in Lebanon that ended inconclusively with a U.N.-brokered truce.
The agreement came days before Bush is due to the visit the Middle East, stopping in Jordan for talks expected to touch on the Israeli-Palestinian conflict as well as Iraq. Progress in bringing Israelis and Palestinians together could provide relief for Washington from the troubles in Iraq.