Jerusalem - The Israeli military extended its air campaign in the Gaza Strip on Monday, and the nation's defense minister warned that the country is in "an all-out war" with its Hamas adversaries, who control the Palestinian territory.

    The three-day death toll in Gaza climbed to 345 with more than 1,400 injured, and Gaza doctors said they were running out of blood, bandages and other supplies.

    Israel's air strikes failed, however, to prevent the deadliest day of Gaza rocket and mortar fire to hit the country.

    Gaza militants fired dozens of crude rockets and killed three Israelis in three separate attacks. Israeli officials said that a relatively sophisticated rocket killed one Israeli in Ashdod, Israel's southern port city about 20 miles north of the Gaza border. A mortar strike near the Gaza border killed a second Israeli, and a rocket fired at the coastal city of Ashkelon killed an Arab-Israeli construction worker.

    It was the highest death toll from Gaza rockets and mortars in a single day. Until Monday, Palestinian rocket fire had killed eight Israelis in the past two years. Since Israel launched the air strikes on Saturday, four Israelis have been killed in attacks from Gaza.

    As Israeli tanks, artillery batteries and troops stepped up preparations for a possible ground offensive, Defense Minister Ehud Barak announced that the attacks wouldn't end until the military had delivered a "severe blow" to Hamas.

    "We are in an all-out war against Hamas," Barak told a special session of the Knesset, the Israeli parliament.

    In three days of air strikes, Israel has hit scores of Gaza targets and created a climate of fear among the 1.5 million Palestinians who live in the densely populated Mediterranean coastal strip.

    Gaza families were sleeping in stairwells and corridors in hopes of avoiding the Israeli air strikes, which have targeted Gaza City's largest university, as well as mosques that Israel claimed were being used to store weapons, build rockets or hide militants. Israel announced Monday that it would also attack private residences if they're used to house militants.

    "The IDF will continue to act against anyone who harbors terror in their residence, provides shelter to terrorists and their activities, and forces their children and spouses to act as human shields," the Israeli military said in a statement.

    In messages that have left many Palestinians rattled, Israel has been placing calls to Gaza residents to personally warn them that their homes, or adjacent buildings, were targets.

    Among those trapped in their homes was Wafa Kannan, a 27-year-old Gaza City resident who's been camping out in a narrow apartment corridor with her mother and two brothers since the strikes began on Saturday.

    Over the weekend, Kannan's mother received a recorded call on her cell phone from the Israeli military. When she heard who was calling, she hung up. Minutes later, the same call came to the landline in her apartment warning her to leave if she was storing weapons.

    In an apartment building across the street from Kannan and her family live four brothers who are Hamas militants. Israeli intelligence called the Hamas members to warn them that they were targets, Kannan said.

    Leaders at the local mosque urged neighbors to converge on the apartment building and act as human shields, she added. No one heeded the call, however, so the Hamas militants fled.

    While many families have fled the neighborhood, Kannan said that she and her family don't think there's anywhere to hide from the Israeli strikes.

    "You are not safe anywhere in Gaza," Kannan said in a telephone interview from Gaza. "If it's dangerous in our house, it's dangerous in other houses too."

    The Israeli military said that it was trying to minimize civilian casualties and noted that Hamas itself has acknowledged that most of those killed were members of its security forces.

    On Monday, the United Nations Office for the Coordination of Humanitarian Affairs reported that about a third of those killed as of Sunday afternoon - about 90 Palestinians - were civilians.

    Israel also allowed 63 truckloads of aid and 1,000 units of blood into Gaza to replenish dangerously low supplies.

    United Nations Secretary-General Ban Ki-moon called Monday for an immediate cease-fire, but neither Hamas nor Israel showed any signs of working towards a political compromise.

    Israeli government leaders made it clear that they want to contain the rocket fire from Gaza, but have yet to explain when or how this conflict will come to an end.

    "The strategy today is to hit Hamas, and to hit Hamas hard," said Mark Regev, a spokesman for Israeli Prime Minister Ehud Olmert. "We believe that will create a new reality, a new security environment in which a quarter million Israelis no longer have to live in fear of rocket attacks."

    Regev said that Israel wasn't actively looking to topple Hamas, the Islamist militant group that seized control of the Gaza Strip in a June 2006 military showdown with fighters loyal to Palestinian Authority President Mahmoud Abbas.

    "We have not articulated regime change as a strategic goal," Regev said of Hamas, which was founded in part to destroy Israel.

    The internal Palestinian rift has deepened in the past 18 months, and Abbas pointedly blamed Hamas over the weekend for bringing the Israeli attacks on itself by not agreeing to renew a six-month cease-fire that brought temporary and relative calm to the area until it expired earlier this month.

    In apparent preparation for sending in troops, Israel Monday declared large swaths of its border with Gaza "closed military zones" that prohibit journalists and others from entering.

    Last month, Israel shut its main border crossing with Gaza to all-but- essential medical cases.

    As it did during the first phase of Israel's 2006 war with Hezbollah in Lebanon, the Israeli public has rallied behind the air strikes. Polls show growing Israeli support for the attacks on Hamas.

    That backing could plummet, however, if Israel embarks on a ground offensive that ends with heavy casualties and no clear-cut victory as the one in Lebanon did.

    "I don't think Israel is looking for a political solution," said Yossi Kuperwasser, the brigadier general who served as head of the Israeli military's intelligence branch during the 2006 war. "Israel is looking for a situation where Hamas, because of its own considerations, decides not to shoot."

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    Hamda, a McClatchy special correspondent, reported from Gaza City.