GAZA CITY, Gaza Strip "“ Palestinian militants sent a deadly barrage of missiles flying deep into Israel on Monday, demonstrating that Hamas still had firepower three days into Israel's punishing air offensive in Gaza.

Four Israelis, including a soldier, were killed and eight wounded. Palestinian health officials put the three-day death toll in Gaza at 364; the U.N. said the total included at least 62 civilians.

In Monday's attacks, Israel focused its bombing on the houses of Hamas field operatives in a campaign meant to tear at the roots of the extremist group ruling Gaza. Israel's defense minister promised a "war to the bitter end against Hamas" and allied militants.

Early Tuesday, Israeli aircraft dropped at least 16 bombs on five Hamas government buildings in a Gaza City complex, destroying them, setting fires and sending rubble flying for hundreds of yards, witnesses said. Rescue workers said 40 people were injured.

Intensified rocket strikes by Gaza militants, which triggered the Israeli offensive, have revealed the expanding range of missiles that are making larger cities farther inside Israel vulnerable.

In a barrage Monday night, a missile crashed into a bus stop in Ashdod, 23 miles from the Gaza Strip. A woman died and two others were wounded, one seriously "” the first casualties in the city of 190,000 residents.

The military said an Israeli soldier was killed later in a mortar strike, the first soldier to be killed in the conflict. Five others were wounded, one seriously, according to a military statement.

Earlier Monday, an Israeli was killed and one seriously wounded by a rocket strike in the Negev desert community of Nahal Oz, closer to the Gaza border. A rocket also killed an Israeli construction worker in the city of Ashkelon. In all, five Israelis have been killed since the Gaza offensive began Saturday, bringing to 19 the number killed in rocket attacks from Gaza this year.

Early Tuesday, Hamas released a statement saying its squads had fired 43 homemade rockets, 17 longer-range Grads and six mortar shells at Israel. Other militant groups also fired rockets at Israel.

The targets chosen by Israel on Monday pointed to an intention to chip away at Hamas' foundation. Israeli aircraft staged five separate strikes on the houses of field operatives, though there was no confirmation that any of them were killed.

A grainy video taken by an Israeli drone airplane showed several men loading a pickup truck with what the Israeli military said were medium-range Grad rockets. Moments later, a big explosion from an Israeli missile strike envelops the image.

One Israeli attack targeted a house in the Jebaliya refugee camp, killing seven people, but the Hamas activist was not there, Hamas security and relatives said. Another hit the Jebaliya home of Abdel-Karim Jaber, a Hamas political figure who is a senior administrator at Gaza's Islamic University. He was not at home and it wasn't immediately clear if anyone was hurt in the strike.

In another air assault, an Islamic Jihad commander was killed as he was walking near his house, said Abu Hamza, a spokesman for Islamic Jihad's military wing.

Israel's airstrikes on more than 325 sites since midday Saturday reduced dozens of buildings to rubble, overwhelmed hospitals with wounded and filled Gaza's deserted streets with smoke and fire. The military said Israeli naval vessels had also bombarded targets from the sea.

On Monday, aircraft pulverized a house next to the home of Hamas Premier Ismail Haniyeh, a security compound and a five-story building at a university closely linked to the Islamic group "” all symbols of Hamas strength in the coastal territory it has ruled since June 2007.

Israel's offensive has rattled the Middle East and capitals around the world, triggering street protests and fiery speeches by adversaries of Israel like the militant group Hezbollah in Lebanon. In the day's biggest outpouring of anger, tens of thousands of Hezbollah's supporters stood in a pouring rain in a Beirut square to condemn Israel.

Stone-throwing clashes broke out in about a half-dozen spots in the Palestinians' West Bank territory as well as in several Arab-populated areas inside Israel. Israeli police and soldiers fired rubber bullets and tear gas at rioting youths, but it did not appear anyone was injured.

U.N. Secretary-General Ban Ki-moon condemned Israel's offensive as excessive and demanded an immediate cease-fire. He said key international and regional players "” including foreign ministers of the Arab League nations holding an emergency meeting Wednesday "” must "act swiftly and decisively to bring an early end to this impasse."

The U.S. government said it was "vigorously engaged" in trying to restore a cease-fire.

White House spokesman Gordon Johndroe defended the Israeli response, but added that the Bush administration was urging Israel to avoid civilian casualties in Gaza.

With Israeli troops and tanks massing on the Gaza border, Defense Minister Ehud Barak told parliament he wanted to strike a devastating blow against Hamas. However, later he indicated a ground assault was not inevitable, issuing a warning that he was giving Hamas a last chance to halt its rocket fire.

Speaking in Hebrew, Barak told the lawmakers: "We have a war to the bitter end against Hamas, and the home front, which has turned into a battlefront, will continue to be a source of strength for the Israeli military." Some news organizations translated the start of the quote as saying "an all-out war on Hamas."

Short of reoccupying Gaza, however, it was unlikely any amount of Israeli firepower could completely snuff out militant rocket attacks. Past operations all failed to do so.

The Cabinet's decision over the weekend to call up 6,500 reserve soldiers could be a pressure tactic. Military experts noted no full combat units had been mobilized and said Israel would need at least 10,000 soldiers for a full-scale invasion.

For the first time, Israel also hit one of a series of tunnels prepared by Hamas along the border with Israel for use in attacks on invading ground troops, several Israeli TV networks said. One tunnel was packed with explosives and several militants inside were killed, Channel 1 said.

Most of those killed in three days of airstrikes were Hamas members. A Hamas police spokesman, Ehab Ghussen, said 180 members of Hamas security forces were among the dead.

But the U.N. agency in charge of Palestinian refugees expressed concern about civilian casualties. A rise in civilian casualties could intensify international pressure on Israel to end the offensive.

In New York, U.N. humanitarian chief John Holmes said his agency had not been able to determine a precise number of civilian casualties, but knew of at least 62 women and children killed. He said 1,400 people had been injured.

Eight children under the age of 17 were killed in two separate Israeli airstrikes Sunday night, Palestinian medics said.

Holmes said he was very worried about a shortage of humanitarian supplies in Gaza.

"Because of the effective blockade that's been in place for many months now, and because of the increasing tightening of this blockade in recent weeks around Gaza, stocks of vital items are either very low or nonexistent, and that's particularly the case, for example, with wheat flour," he said.

Israel opened one of Gaza's border crossings Monday to allow several ambulances and 62 trucks carrying medical supplies and food to cross.

"Obviously these supplies are better than nothing, but they remain wholly inadequate," Holmes said, saying that his agency needed 100 truckloads of flour every day to meet needs.

In Gaza, some families left their apartments next to institutions linked to Hamas, fearing they could be targeted. Suad Abu Wadi, 42, kept her six children close to her on mattresses in her Gaza City living room. Her husband sat with them, chain-smoking. Abu Wadi said he had not said a word since seeing their neighbor carrying the body of his child, killed in an airstrike Saturday.

Gaza's nine hospitals were overwhelmed. Dr. Moaiya Hassanain, who keeps a record for the Gaza Health Ministry, said 364 Palestinians had died and more than 1,400 wounded. Some of the injured were being taken to private clinics and even homes, he said.

Egyptian officials said ambulances were ferrying wounded Gazans to hospitals in Egypt from Gaza's Rafah border crossing. Tariq al-Mahlawi, Egypt's deputy health minister, said 32 patients had been brought in by nightfall and that 500 beds were ready to treat Palestinians.

Around mid-afternoon, ambulances ferried the wounded from Gaza toward the crossing in the border town of Rafah, where over a dozen Egyptian ambulances waited to take over the casualties.

Despite Israel's battering attacks, sirens warning of incoming rockets sent Israelis scrambling for cover throughout the day as more than 40 rockets and mortar rounds rained down.

Israeli security officials warned that the militants' rockets are powerful enough now to reach Beersheba, a major city 30 miles from Gaza.

Mazal Ivgi, a 62-year-old resident of Beersheba, said she had prepared a bomb shelter. "In the meantime we don't really believe it's going to happen, but when the first boom comes people will be worried," she said.

___

Associated Press writers Aron Heller in Ashkelon, Jason Keyser in Jerusalem, Edith M. Lederer in New York, Deb Riechmann in Crawford, Texas, and Omar Sinan in Rafah, Egypt, contributed to this report.