The Israeli Security Cabinet met early Tuesday morning and reached a decision to halt aerial strikes beginning at 9 a.m. (2 a.m. ET).
"We remain alert and preserve high preparedness levels, both defensive and offensive," military spokesman Peter Lerner said. "If the Hamas terror organization will fire at Israel, we shall respond."tweeted.
The plan calls for all sides to cease hostilities in Gaza. It also calls for the opening of border crossings, once the security situation is stable, and for high-level talks among those involved.
Hamas' military wing, the Qassam Brigades, dismissed any talks of a cease-fire, saying its battle with "the enemy" will "increase in ferocity and intensity."
"We in the Al-Qassam Brigades reject altogether the proposal, which for us is not worth the ink that it was written with."
Since the Cabinet's announcement, rocket fire continued from Gaza into its territory, the Israeli military said.
Hanan Ashrawi, a member of the Executive Committee of the Palestinian Liberation Organization, said the Israeli acceptance of the Egyptian proposal should be seen as "a first step, not the end."
"We have to be cautious of this cycle of violence which the Palestinian people continue to suffer," she said.
U.S. President Barack Obama on Monday welcomed Egypt's proposal, saying he hoped it would "restore the calm that we've been seeking."
Earlier, Hamas mocked the proposal in public, with a spokesman describing it as a "joke."
"We did not receive this declared paper from the Egyptians ... which means it's an initiative for the media. It's not a political initiative," said Osama Hamdan.
Speaking on CNN's "The Situation Room with Wolf Blitzer," he continued: "It's not really an initiative. It's not really an idea, what they are trying to do is to corner the Palestinians and to help the Israelis more."
The stakes are high and climbing.
By Tuesday, the death toll from a week of Israeli airstrikes on Gaza had reached 194 with at least 1,400 wounded, according to Palestinian health authorities.
The death toll is now greater than the number of people killed in Gaza during the 2012 conflict between Israel and Hamas.
Amid the diplomatic maneuvering, the residents of Gaza are stuck in the middle of the continued fighting. The United Nations has said that most of the people killed by Israel's aerial attacks are civilians.
"I urgently call on the Israeli Security Forces to put an end to attacks against, or endangering, civilians and civilian infrastructure which are contrary to international humanitarian law," said Pierre Krahenbuhl, commissioner general of the United Nations Relief and Works Agency for Palestine Refugees, or UNWRA.
There are now 17,000 refugees taking shelter in 20 schools in Gaza, UNWRA said, and the airstrikes have damaged 47 of its buildings, including clinics, schools and warehouses.
The Israeli military says it uses a variety of methods, including phone calls and leaflets, to warn civilians of impending strikes.
But UNWRA called on Israel to exercise maximum restraint and precaution to avoid more casualties.
"Clearly at this stage not enough is being done in that regard," Krahenbuhl said.
Israel said Monday its forces have struck 1,470 "terror targets" across Gaza, including 770 concealed rocket launchers.
But in one area of northern Gaza, Mohamed Abu Hassan said Monday he doesn't understand why his house was severely damaged in an Israeli airstrike that struck the building next door.
There was no unusual activity in the house in the town of Jabalya, he said.
"My son isn't even here. He's working in Libya," Hassan said. Only his wife is at the house.
"Is she fighting Israel?" he asks. "This is tyranny."
Israel has used its Iron Dome defense system against some of the more than 1,088 rockets fired from Gaza into Israel, the military said.
On Monday, the system intercepted a rocket fired from Gaza toward the Israeli border town of Sderot, close to CNN's Blitzer.
"We heard a loud boom," he said. "If you don't seek shelter, you're gonna be in danger because even though the rocket was destroyed in the air, the shrapnel starts coming down very, very quickly."
When sirens go off, people along the border have about 15 second to seek shelter. Farther north in Tel Aviv, where the Iron Dome system also intercepted a rocket Monday, people have about a minute.
Seventy percent of Israel's population lies within range of Hamas rocket attacks, according to the Israel Defense Forces. The defense system has intercepted roughly a fifth of the rockets fired, the IDF said early Tuesday.
So far, no Israelis have been killed by the rocket attacks.
Secretary of State John Kerry was preparing a possible trip to the Middle East to lay groundwork for a cease-fire, but several U.S. officials told CNN Monday night that Kerry is postponing the visit to give Egyptian efforts a chance to take root.
One official said the United States wants to give Egypt a chance to reassert itself as a power broker the Middle East, as it did during the 2012 cease-fire.
The current Egyptian President, the ex-military chief Abdel Fattah al-Sisi, has weaker relations with Hamas than former President Mohammed Morsy, who brokered the 2012 deal. Morsy was ousted by the military in 2013.
Earlier, Kerry spoke by phone with Netanyahu and expressed U.S. concerns about escalating tensions. He reiterated that the U.S. is prepared to help bring about a cease-fire, a senior State Department official said.
But "offering facilitation is not enough," Yousef Munayyer of the Washington-based Palestine Center told CNN's "New Day."
"It's important that the United States demand a cease-fire," he said. "There is no military solution to this."
Israel will press its air and ground offensive in the Gaza Strip, Prime Minister Benjamin Netanyahu said Monday, preparing his country for a longer and bloodier campaign and dashing hopes that the three-week-old conflict would end soon.
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