JERUSALEM (CNN) -- Israel has declared a unilateral cease-fire in the fighting in Gaza beginning at 2 a.m. Sunday (7 p.m. ET Saturday), Israeli Prime Minister Ehud Olmert said.
A man escapes after an Israeli strike in Beit Lahia in northern Gaza on Saturday.
"Hamas has been dealt a very serious blow," Olmert said. "We can say that the conditions have been brought about that enable us to say that the aims that we laid down for the operation have been completely achieved."
Yet Israel is prepared to respond if Hamas militants continue fighting in the Palestinian territory, Olmert said.
"If foes decide to continue to fight against us, then we will be ready and we shall consider ourselves justified in replying," he said. "I do not suggest that Hamas or other terrorist organizations try us."
Immediate Palestinian response to Olmert's announcement was pessimistic.
Saeb Erakat, the chief Palestinian negotiator involved in diplomatic talks on the conflict, noted that Olmert did not say Israeli troops would be leaving Gaza.
"I'm afraid this means the cease-fire will not stand; it will break," Erakat told CNN International. "Anybody can fire a shot now. ... It's a very fragile moment."
The announcement followed a Cabinet meeting Saturday meant to vote on the basics of a plan that could end fighting in Gaza. It also came a day after Israeli and U.S. diplomats signed an agreement designed to stop arms smuggling into the Palestinian territory through tunnels.
Israel launched the offensive in Gaza three weeks ago with the stated intent of stopping rocket fire into southern Israel from Hamas fighters in Gaza.
There is mounting international pressure to end the fighting.
In a televised speech Saturday, Egyptian President Hosni Mubarak called on Israel to end military operations and withdraw from Gaza. He dismissed the idea of an international force based in Egypt, saying he would "never accept" a foreign presence on Egyptian soil.
U.N. Secretary-General Ban Ki-moon also reiterated his call for a cease-fire during a speech before the Lebanese parliament Saturday.
"The level of violence in Gaza is unprecedented," the U.N. chief said. "The Israeli aerial and land offensives against Hamas targets are inflicting heavy civilian casualties, widespread destruction and tremendous suffering for the entire region." Watch opinions from the iReport community »
The three-week conflict has killed 1,203 people in Gaza and injured more than 5,000 more, many of them Palestinian civilians, according to medical sources in Gaza City. They said 410 children have died.
On the Israeli side, 10 soldiers and three civilians have been killed and more than 200 soldiers have been wounded since the fighting began, an Israel Defense Forces spokesman said Saturday.
Fighting continued as the IDF attacked 50 targets between Friday night and Saturday morning, including eight missile-launching sites and 70 tunnels along the Egyptian border. The IDF says the tunnels were being used by Hamas to smuggle weapons into Gaza.
Two children were killed in an Israeli artillery attack at a U.N. school north of Gaza City early Saturday.
"This yet again illustrates that there is no place safe in the Gaza Strip," said Chris Gunness, a U.N. spokesman, speaking of the attack. "This fighting has to stop, because innocent people, women and children, who are taking refuge in neutral U.N. buildings are discovering that there is nowhere safe." Watch a report on aid shortages to Gaza »
Four IDF soldiers were seriously wounded early Saturday by mortar fire in Gaza, according to an IDF statement.
Hamas has said a cease-fire alone is not enough.
"We are working in every direction so we can achieve our objectives in stopping the aggression, lifting the blockade, opening the crossings, and the compensation of our people and the rebuilding of the Gaza strip," said Hamas delegation spokesman Salah Bardwill.
In other diplomatic efforts, the state of Qatar held an emergency summit Friday in an attempt to find a unified Arab voice on Gaza. The meeting brought together several Arab and Muslim leaders, including the presidents of Iran and Syria and the leader of Hamas, Khaled Meshaal.
Friday evening, the U.N. General Assembly voted 142-4 to call on Israel to abide by a January 8 resolution by the U.N. Security Council.
The resolution, which called for an immediate cease-fire by both sides in the conflict, had been universally ignored.
Israel and the United States were among the countries voting against Friday's effort.
CNN's Ben Wedeman, Paula Hancocks, Elise Labott, Caroline Faraj, Mohammed Jamjoom and Arie Bell contributed to this report.