While the vast majority of casualties are Palestinians in Gaza, Israel continues to ward off rocket attacks from Gaza with its Iron Dome missile defense system. Israeli officials say they are committed to destroying tunnels used by Palestinian militants in Gaza to make their way into Israel.
A poll released this week showed 86.5% of Jewish Israelis surveyed say Israel cannot accept a cease-fire because "Hamas continues firing missiles on Israel, not all the tunnels have been found, and Hamas has not surrendered," according to the Jerusalem Post.
But Israel's incursion into Gaza has had ripple effects around the world. Chile, Peru, Brazil and Ecuador have pulled their ambassadors out of Tel Aviv to protest the Israeli offensive.
It's unclear how many in Gaza want militants to stop rocket attacks.
Last month, a poll by the Washington Institute for Near East policy found most Palestinians in Gaza oppose a two-state solution and want to work toward a five-year goal of abolishing Israel. But the majority said they support nonviolent methods of "popular resistance."
Most Israelis support a two-state solution, according to a poll by the Dialog Institute, Haaretz reported.
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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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Deadly clashes broke out after Israeli tanks drove into Gaza and launched a ground operation that escalates the conflict with Hamas.
The incursion Thursday night follows 10 days of Israeli bombardment of Gaza that has killed more than 250 people. Israel launched the aerial offensive last week, saying it aimed to halt the firing of Hamas rockets from Gaza into Israel.
Israeli Prime Minister Benjamin Netanyahu and Defense Minister Moshe Yaalon ordered the ground operation to destroy tunnels dug from Gaza into Israeli territory, according to a statement.
Thirteen Hamas militants used a tunnel earlier Thursday to launch an attempted attack in Sufa, near an Israeli kibbutz, but were stopped by Israeli soldiers, the Israel Defense Forces said.
The IDF said it had sent a "large" force into Gaza that includes infantry, tanks, artillery, combat engineers and intelligence units, with aerial and naval support.
CNN's Wolf Blitzer asked Mark Regev, Netanyahu's spokesman, whether Israel planned to occupy Gaza for a long time.
Regev didn't answer directly, but said Israel's goals are to "diminish" the Hamas military force and to show that it cannot attack Israel with impunity.
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At least three mortars were fired from Gaza toward southern Israel on Thursday morning, some two hours after a temporary lull in hostilities went into effect to allow humanitarian supplies into the area.
The mortars fell in open areas and no injuries were immediately reported, the Israeli military said. Mortars are smaller and have a more limited range than rockets.
Israel, which said it would honor the cease-fire but not sit idle if attacked, did not immediately respond.
The five-hour long temporary halt in fighting went into effect at 3 a.m. ET, requested by the United Nations to offer a brief respite in a conflict that has killed more than 220 people.
Banks opened for the first time in 10 days in Gaza and residents poured into the streets.
Red Cross officials visited hospitals and damaged houses to assess medical needs, and worked with local officials to quickly fix water pipelines, which has left hundreds of thousands without water.
There were no reported air strikes since the cease-fire began. Still, the fear of death hung heavily over Gaza. The health ministry warned civilians to avoid gathering in squares.
"Should the humanitarian window be exploited by Hamas or other terror organizations for the purpose of launching attacks against Israeli civilian or military targets the IDF will respond firmly and decisively," the Israeli military 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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One bomb dropped on a center for the disabled. Another wiped out 18 members of the same family.
By Monday morning, the death toll from nearly a week of Israeli airstrikes on Gaza had reached 172 - all of them Palestinians - with more than 1,250 wounded, according to Palestinian health authorities.
Israel has so far shrugged off international calls for a cease-fire, saying it will continue the offensive as long as the militant group Hamas keeps firing rockets into its territory.
And Hamas shows no sign of letting up after already launching almost 1,000 rockets at Israel.
Caught in the middle are the residents of Gaza. While the Israeli attacks have killed some militants, around 70% of the fatalities were civilians, according to the United Nations. Of the dead, more than 30 are children, the U.N. reported.
"All sides ... must respect the sanctity of civilian life," said Chris Gunness, spokesman for the United Nations Relief and Works Agency for Palestine Refugees.
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Israel faced attack from a second front Friday, but it is unlikely that a rocket fired from Lebanon signifies the widening of a conflict that has left at least 100 dead in Gaza.
The rocket launched from Lebanon landed near the northern Israeli town of Metula, which sits right by the Lebanese border, and no damage or injuries have been reported. It was not immediately clear who fired the rocket.
An Israel Defense Forces spokesman said Israel holds the Lebanese government responsible for the attack, but concerns that Israel will face a two-front conflict are unlikely to be realized.
Hezbollah, which operates in Lebanon and is caught up in other conflicts in the region, probably does not have the appetite to start a war with Israel.
Thousands of rockets were fired from Lebanon into Israel during a war in 2006, but rocket attacks since then have been sporadic. Tensions are always high between Hezbollah and Israel, but Hezbollah's involvement in Syria's civil war means that a fight with Israel might not make sense.
Nonetheless, Israel responded with artillery that landed in the vicinity of the Lebanese town of Kfar Shouba. No casualties were reported, the Lebanese army said.
Israel continued to weather rocket attacks by the Palestinian group Hamas in Gaza, but virtually all of the casualties in the conflict have been suffered on the Gazan side.
Though menacing, nearly all the Hamas rockets have been intercepted by the Israeli air defense system or struck empty areas. Airstrikes by Israel in Gaza, in contrast, have been blamed for at least 100 deaths, including 22 children and 20 women, a spokesman for Gaza's Ministry of Health said.
Hospitals in Gaza are unable to take care of the wounded - who top 700 - and patients are being treated on the floors because emergency rooms are overcrowded, medical sources told CNN.
The same medical sources said that medicines are running low and that the scenes at the hospitals are not unlike the chaos witnessed at Syrian hospitals during its civil war.
CNN staff in Gaza reported there are rolling blackouts, and there are water shortages in some areas because airstrikes have damaged pumping stations.
The Israeli military, meanwhile, said that some 100 rockets were fired at Israel today, including one that was intercepted over the Tel Aviv metropolitan area.
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The dark curtain rises again on the tragedy of Israel and Gaza, and the next act begins much like its forerunners.
Rockets hunt humans. Bombs crush buildings. Blood spills. The dead ride in caskets through streets, and mothers wail their grief to the heavens.
As Israeli reserves gather like a storm over Gaza's horizon, the added bloodshed of an incursion appears imminent, and millions watching around the world ask: What could they hope to achieve?
There is no dramatic endgame in this, but there are concrete objectives, says Israeli military analyst and columnist Ron Ben-Yishai.
There are official ones and unofficial ones, short-term and long-term, that make sense for Israel, he argues.
Many of them will work, concedes critical Israeli columnist Gideon Levy. But he disagrees about their wisdom.
They won't cure the disease but instead feed it, he argues.
Military objective No. 1
First, the conservative government led by Prime Minister Benjamin Netanyahu wants to stop the rocket fire by force.
And weaken the Hamas militants and other groups behind it, Ben-Yishai says.
"Erode the political clout and the ability of Hamas to act both as a political and military-terrorist movement."
Those are the official goals given by the Cabinet for the military operation named Protective Edge, he says. And they'll probably be achieved, Ben-Yishai says.
"For the short-run, no doubt," Levy concurs. But he also thinks Hamas will come back stronger militarily and politically.
That's what happened over two years ago in operation Pillar of Defense and over five years ago in Operation Cast Lead, he says.
In the latter, 1,300 Palestinians and more than a dozen Israelis died.
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