Fierce fighting between Israeli troops and Hamas militants continued near Gaza City on Monday as the death toll from the conflict rose above 500.
Heavy bombardment hit areas east of the city, particularly the neighborhood of Shaja'ia, where a large Israeli assault Sunday contributed to the deadliest day of the war so far.
As clashes escalated over the weekend, Hamas said it had captured an Israeli soldier - a claim Israel later denied.
With no sign of either side backing down in a conflict in which most of the victims have been civilians, U.S. Secretary of State John Kerry is due to arrive in Egypt on Monday to push for a cease-fire.
Speaking to CNN's "State of the Union" on Sunday Kerry said that the United States supports Egypt's initiative for a truce and "will work for a fair cease-fire."
The United States has "shown our willingness to try to deal with the underlying issues," but Hamas "must step up and show a level of reasonableness," he said.
"No country, no human being, is comfortable with children being killed, with people being killed, but we're not comfortable with Israeli soldiers being killed either or with people being rocketed in Israel," Kerry said.
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The Israeli Defense Forces said Wednesday that it warned residents of three areas in Gaza to vacate their homes because of its plans to carry out airstrikes on Hamas and other terrorist groups.
The IDF said it used recorded messages, text messages and leaflets to alert the populations in Beit Lahyia, Shuja'iya and Zeitoun, places where it said "a high volume of rocket fire at Israel has originated."
"We are all scared but we are force to live in this and there is nothing for us to do," said Abu Musbah, a, 21-year-old member of Islamic Jihad, one of the groups that is firing rockets at Israel. "The children are scared but we struggle to continue our lives."
He said he had already evacuated all of his family members from his house in Shuja'iya.
A woman in the southern Gaza town of Khan Yunis said some people had fled there from harder hit areas in the north and east of the territory, filling some homes with multiple families.
"Those who have family here have come," said the woman, who asked not to be identified for fear of repercussions from talking to the news media.
She said she believed other people were staying in their houses, regardless of warnings from lsraeli leaflets or other means.
These are their homes, they will not run, she said.
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Israel says it has accepted an Egyptian proposal for a cease-fire with Hamas. But without the militant group signing up as well, there may be little hope of seeing an end to the near constant exchange of fire that has so far killed more than 190 Palestinians in Gaza.
The Israeli security cabinet met early Tuesday morning and released a statement that said, "The cabinet has decided to reply positively to the Egyptian initiative for a ceasefire at 9 a.m. (2 a.m. ET)."
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 officials did not immediately respond to the cabinet's decision. But since the cabinet's announcement, only one rocket was fired from Gaza into its territory, the Israeli military said.
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."
Hamas' military wing, the Qassam Brigades, said it hadn't received any formal or informal request about a cease-fire. But it said it rejects the proposal, describing it as an initiative of "kneeling and submission."
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