The prime minister added: “In the past few weeks the Israeli and Palestinian offices have been in constant contact, and there are understandings; but these must mature into negotiations, and I hope this will happen soon.
Olmert and Vice Premier Shimon Peres visited Rahat for the inauguration of a high school in the city.
Olmert recounted the decision on the ceasefire, saying, “Last night (Saturday) the head of the Palestinian Authority (Mahmoud Abbas) called to inform me of the Palestinian factions’ decision on a ceasefire, the cessation of all acts of violence, including arms smuggling through tunnels, sending suicide bombers and firing Qassams.
“We both agreed that both sides would make every effort so this ceasefire would go into effect this morning,” he said.
Olmert added that he took into account that ceasefires are not immediately implemented but "I ordered all IDF forces to leave the Gaza Strip. Although there are still breaches from the other side, I ordered troops to show restraint and to give the ceasefire a chance."
He also said: "Hamas said this morning that we are not in talks with them, because firing Qassams is a violation of the commitment. The State of Israel is a strong country and it has enough power to fight terror and also to show restraint and give a chance for the ceasefire to take hold, as Abu Mazen promised us. We will show restraint and responsibility, certainly in the coming days."
Sderot protests ongoing Qassam fire
Speaking about the fate of kidnapped soldier Gilad Shalit he said: "Although the ceasefire doesn't provide an answer to all the issues, we hope for the immediate release of Shalit. I believe an understanding over a ceasefire will lead to his release."
"We hope the ceasefire will take hold in Judea and Samaria. At the moment it is not implemented there. If they show responsibility and good will, all this will lead to the commencement of negotiations that are serious, real and openhearted between us and the Palestinian Authority. Over the past few weeks Israeli and Palestinian teams are in constant contact, and there are understandings. All these have to ripen into negotiations, and I hope this will happen soon."
Vice Premier Shimon Peres said: "The problem is not the ceasefire but the tendency. There is no alternative to ceasefire. There is no problem in returning to war, but that is not what we want."
"Abu Mazen has a big role in the ceasefire. I expect difficulties and I don't think it is easy, there are five to six groups here and it is difficult to bridle all of them. But Hamas understood that it has no chance of managing its affairs with its face to fire and its back to peace."
But the optimism that the two leaders expressed did not reach Sderot residents who were not impressed with the ceasefire especially as rocket fire continued ours after the ceasefire went into effect.
Residents burnt tires upon hearing that Olmert plans to visit the city.
The head of the Sderot struggle headquarter, Alon Davidi said residents have little hope the ceasefire will hold.
"Unfortunately the Israeli government chooses an easy solution on every occasion by turning to Abou Mazen, and every time Sderot residents wake up to a difficult reality. All ceasefire agreement signed so far, were fully respected by us but were not respected by the other side. At then the Palestinians will use the ceasefire to rearm."
Anat Breshkovsky contributed to the report