JERUSALEM - The Israeli military extended its air campaign in the Gaza Strip yesterday, and the nation's defense minister warned that Israel was in "an all-out war" with its Hamas adversaries, who control the Palestinian territory.

The three-day death toll in Gaza climbed past 350 with more than 1,400 injured, and doctors there 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 extremists fired dozens of crude rockets and killed three Israelis in three attacks. Israeli officials said a relatively sophisticated rocket killed one Israeli in the southern port city of Ashdod, 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 yesterday, Palestinian rocket fire had killed eight Israelis in years. Since Israel launched the air strikes 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 said the attacks would not 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, Israel's parliament.

In three days of air strikes, Israel has hit scores of Gaza targets - including government ministries, police compounds, and smugglers' tunnels - 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 air strikes, which have targeted Gaza City's largest university, as well as mosques that Israel contended were being used to store weapons, build rockets, or hide extremists.

Israel said yesterday that it would also attack private residences if they are used to house extremists.

Israeli forces "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 military said in a statement.

In messages that have rattled many Palestinians, 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, 27, of Gaza City, who has been camping out in a narrow apartment corridor with her mother and two brothers since the strikes began.

Over the weekend, Kannan's mother got 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.

Four brothers who are Hamas members live in an apartment building across the street. Kannan said Israeli intelligence called them to warn them they were targets.

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 fighters fled.

While many families have left the neighborhood, Kannan said her family did not think there was anywhere to hide from Israeli strikes.

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

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

Yesterday, the U.N. Office for the Coordination of Humanitarian Affairs said 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.

U.N. Secretary-General Ban Ki-moon called yesterday for an immediate cease-fire, but neither Hamas nor Israel showed any signs of working toward a political compromise. European Union foreign ministers agreed to meet in Paris today for emergency talks over the situation, Bloomberg News reported.

Protesters rallying against the air strikes took to the streets yesterday in Beirut, Tehran, and other cities in the Middle East and Europe.

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

"The strategy today is to hit Hamas, and to hit Hamas hard," said Mark Regev, a spokesman for 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."

Hamas seized control of Gaza in a June 2006 military showdown with fighters loyal to Palestinian Authority President Mahmoud Abbas. Abbas and his Fatah faction still control the West Bank.

The internal Palestinian rift has deepened in the last 18 months, and Abbas 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 this month.

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

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.