French President Nicolas Sarkozy said in Paris that both Israel and the moderate Palestinian leadership in charge of the West Bank had accepted the truce proposal, but Israeli officials did not confirm that.
In Turkey, meanwhile, a diplomat said that country will be given the task of constructing an international force for Gaza.
Both Israel and Hamas appeared to seek guarantees about the details of a cease-fire, before agreeing to halt the fighting.
Israel said it would support the proposal only if it halts "hostile fire" from Hamas in Gaza and includes measures to prevent the militant group from rearming, said government spokesman Mark Regev.
"Israel welcomes the initiative of the French president and the Egyptian president to bring about a sustainable quiet in the south," he said.
Hamas said Israel does not seem to be serious about reaching a cease-fire."Israel is still widening and escalating its aggression and is not giving any positive signals in response to these efforts," Ghazi Hammad said.
The precise details of the Egyptian-French proposal remain unclear, but it comes as international outrage grows over civilian deaths in Gaza.
About 300 of the more than 670 Palestinians killed so far were civilians, according to Palestinian and U.N. figures. Of those killed, at least 130 are children 16 and younger, says the Gaza-based Palestinian Center for Human Rights, which tracks casualties.
Israel has lost six soldiers since launching a ground offensive on Saturday - four of them in "friendly fire" incidents - and four other Israelis have been killed by rocket fire, three of them civilians, since fighting began on Dec. 27.
With Gazans increasingly suffering the effects of nonstop airstrikes and shelling, Israel's military said it would open "humanitarian corridors" to allow aid to reach Palestinians.
Israeli military spokesman Peter Lerner said the 1 to 4 p.m. "recess in offensive operations" was aimed at allowing in supplies and fuel. He said similar lulls in the coming days would be considered.
Lerner said that even during the pause, "For every attack against the army, there will be a response." The scale of fighting appeared to drop after the lull took effect, gaining in scope again when it expired.
Before Wednesday's brief lull, Israel said it struck 40 Hamas targets overnight. Gaza health officials said strikes Wednesday morning killed eight people.
Outrage grew over an Israeli shelling Tuesday near a U.N. school, with the U.N. agency responsible for the building demanding an "impartial investigation" into the attack. Gaza health officials put the death toll from the strike at 39, while the U.N. says 40 were killed in the deadliest single strike of the fighting.
Israel says its forces fired at militants who launched mortars from that location.
The number of Palestinian fighters killed is unclear, as Hamas is keeping its casualties secret.
Israel's lull in operations brought some relief to civilians in Gaza, where much of the territory has no power or running water, because pumps are dependent on electricity.
More than 500 aid trucks have been shipped into Gaza since operations began. But even when aid crosses into Gaza military operations have prevented officials from distributing it, leading to food shortages in some areas.
A World Bank statement Wednesday said there are growing signs of a severe public health crisis in Gaza because of a shortage of drinking water and an escalating failure of the sewage system.
Militants hit the Israeli city of Ashkelon on Wednesday with a medium-range rocket, causing no casualties. Rocket fire has fallen off somewhat as Israeli troops tighten their hold on Gaza, taking over open areas used to launch rockets, but Gaza residents say militants are still launching from heavily populated areas.
Egyptian President Hosni Mubarak said the initiative he proposed with Sarkozy calls for an immediate cease-fire by Israel and Palestinian factions for a limited period to allow humanitarian aid into Gaza and an urgent meeting of Israel and the Palestinian side on arrangements to prevent any repetition of military action and to deal with the causes.
International Mideast envoy Tony Blair said Tuesday the key to any cease-fire will be an arrangement to stop weapons smuggling over the Gaza-Egypt border.
Turkey will be tasked with putting together an international force in Gaza, according to a Mideastern diplomat familiar with the country's efforts to end the conflict. He said the responsibilities of the force were yet to be determined. He spoke on condition of anonymity because of the sensitivity of the information, and Turkish officials would not immediately comment.
An Israeli lieutenant-colonel near the Gaza border in southern Israel said soldiers overwhelmingly opposed a truce. "We went in and we have to finish it off," said the officer, who spoke on condition of anonymity because military regulations forbid him from speaking to the press.
Hamas remained defiant. "This aggression must cease. The blockade must be lifted. The crossings must be unconditionally open. The oppression of our people must end. After that, we can talk," Hamas spokesman Fawzi Barhoum said. He said Wednesday's lull was an Israeli "ruse."
In the meantime, Israel has been making preparations to continue fighting. The military has called up thousands of reserve troops that it could use to expand the Gaza offensive, supporting the three brigade-size formations of regular troops now inside. Defense officials said the troops could be ready for action by Friday. They spoke on condition of anonymity because the army's preparations are classified.
Israel's military said its shelling of the U.N. school - the deadliest single episode since Israeli ground forces invaded Gaza on Saturday following a weeklong air bombardment - was an attack on a military target and accused Hamas militants of using civilians as cover.
Christopher Gunness of the U.N. Relief and Works Agency, responsible for the school, said the agency is "99.9 percent certain there were no militants or military activity in its school."
That would not necessarily contradict Israel's claim that the militants were just outside.
Gunness demanded an investigation, and punishment for anyone found to have violated international law.
Two residents of the area who spoke with The Associated Press by telephone said they saw a small group of militants firing mortar rounds from a street near the school. They spoke on condition of anonymity for fear of reprisal. Gunness said 1,300 people were taking shelter from the shelling at the school.
Barhou, the Hamas spokesman, said there were no militants there at the time.
The Gaza-based Palestinian Center for Human Rights said the presence of militants did not justify Israel's response. "The presence of armed resistance does not justify in any way the use of excessive force that is disproportionate," the center said in a statement.
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Friedman reported from Jerusalem.
