Israel's defense minister said Monday the country is engaged in a "war to the bitter end" against Hamas in the Gaza Strip and said the military operation against the terror group would continue and intensify.

"We have stretched our hand in peace many times to the Palestinian people. We have nothing against the people of Gaza," Ehud Barak said to a special session of parliament. "But this is an all-out war against Hamas and its branches. The restraint that we have demonstrated is the source of our strength when it is time to fight."

Israel's air force obliterated symbols of Hamas power on the third day of its overwhelming Gaza assault, striking a house next to the Hamas premier's home, devastating a security compound and flattening a five-story building at a university closely linked to the Islamic terror group.

In a retaliatory strike, Palestinian militants sent a deadly barrage of missiles deep into Israel, demonstrating that Hamas still had firepower three days into Israel's punishing air offensive in Gaza. Three Israelis were killed and two seriously wounded.

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 casualty in the city of 190,000 residents.

Another Israeli was killed and one seriously wounded by a rocket strike in the Negev desert community of Nahal Oz, closer to the Gaza border. Earlier, a missile killed a construction worker in the city of Ashkelon. In all, four Israelis were dead since the Gaza offensive began Saturday, bringing to 19 the number of people killed in attacks from Gaza since the beginning of the year.

Hamas missiles hit near Ashdod on Sunday, but Monday's attack marked the first time the city suffered casualties from missiles. Ashdod is 23 miles from Gaza, twice as far as the frequent target of Ashkelon and only 25 miles from Israel's heart in Tel Aviv.

Israel declared areas around the Gaza Strip a "closed military zone" Monday, citing the risk from Palestinian rocket fire.

The closure could also help Israel mount a ground assault, as Israeli troops continue to amass at staging sites on the Gaza border and the Cabinet approved the call-up of 6,500 reserve soldiers. Military experts said Israel would need at least 10,000 soldiers for a full-scale invasion.

Click to view photos from the conflict (WARNING: Graphic)

A Hamas police spokesman, Ehab Ghussein, said 180 members of the Hamas security forces were among the dead. The United Nations agency in charge of Palestinian refugees said at least 62 of the dead were civilians. The three-day death toll rose to 364, including eight children under the age of 17 who were killed in two separate strikes overnight, medics said. The U.N. said the total included at least 62 civilians.

Israel launched its deadliest attack against Palestinians in decades on Saturday in retaliation for rocket fire aimed at civilians in southern Israeli towns, which have killed 17 Israelis this year.

Israel is trying to avoid civilian casualties, Foreign Minister Tzipi Livni told reporters Monday, while "Hamas is looking for children to kill."

"Hamas is targeting deliberately kindergartens and schools and citizens and civilians because this is according to their values. Our values are completely different. We are trying to target Hamas, which hides among civilians," Livni said.

A senior Hamas official in Damascus said there is no chance of a new truce with Israel unless all attacks on Gaza cease and the border crossings are reopened.

Moussa Abu Marzouk said Hamas has a right to strike everywhere in Israel and called for Arab countries who have peace treaties with Israel — namely Egypt and Jordan — to sever those ties over the deadly strikes on Gaza.

Hamas, whose charter specifically calls for the destruction of the state of Israel, is listed as a terrorist organization by the United States, Canada, Japan, Australia, the United Kingdon and the European Union and is banned in Jordan.

From 2000 to 2004, Hamas was responsible for killing nearly 400 Israelis and wounding more than 2,000 in 425 attacks, according to the Israeli Ministry of Foreign Affairs.

From 2001 through May 2008, Hamas launched more than 3,000 Qassam rockets and 2,500 mortar attacks against Israeli targets.

Israeli military sources estimated Monday that Hamas' military wing was still intact and that it was capable of carrying out substantial operations in the near future, YnetNews reported.

Three days of strikes have damaged Hamas' ability to launch rockets, but the group still managed to fire dozens Monday deep into southern Israel. One medium-range rocket fired at the Israeli city of Ashkelon killed a man and wounded several others. It was the second fatality in Israel since the beginning of the offensive, and the first person ever to be killed by a rocket in Ashkelon, a city of 120,000.

The White House said Hamas was showing its "true colors as a terrorist organization" and called for it to cease its rocket attacks. "In order for the violence to stop, Hamas must stop firing rockets into Israel and agree to respect a sustainable and durable ceasefire," said National Security Council spokesman Gordon Johndroe.

At first light Monday, strong winds blew black smoke from the bombed sites in Gaza City over deserted streets. The air hummed with the buzz of pilotless drones and the roar of jets, punctuated by the explosions of new airstrikes.

One strike on Monday destroyed the home of the top commander in Hamas's armed wing, killing seven people, including several members of his immediate family.

At least 20 people were injured in the blast, though the target, Hamas chief rocket senior Izz el-Deen al-Qassam Brigades commander, Maher Zaqout, was not at home at the time, Hamas said.

The Israel Defense Forces said Monday that the battle in Gaza was only beginning, and that "the worst is not behind us — it is still ahead of us" during a briefing to southern communities.

"After this operation there will not be one Hamas building left standing in Gaza," said IDF Deputy Chief of Staff Brigadier-General Dan Harel, according to YnetNews.

Israel carried out five separate strikes on the houses of field operatives, though there has been no confirmation that any of them were killed. In another air assault, an Islamic Jihad commander was killed as he was walking near his house.

A group of Iranian hardline clerics volunteered to fight in the Gaza Strip in response to Israel's air strikes, the Fars news agency reported on Monday.

"From Monday the Combatant Clergy Society has activated its Web site for a week to register volunteers to fight against the Zionist regime (Israel) in either the military, financial or propaganda fields," the semi-official news agency said.

Supreme Leader Ayatollah Ali Khamenei issued a religious decree to Muslims around the world on Sunday, ordering them to defend Palestinians in Gaza against Israeli attacks "in any way possible."

One strike destroyed a five-story building in the women's wing at Islamic University, one of the most prominent Hamas symbols. Another attack ravaged a compound controlled by Preventive Security, one of the group's chief security arms, and a third destroyed a house next to the residence of Ismail Haniyeh, the Hamas prime minister. Like other Hamas leaders, Haniyeh is in hiding.

Late Sunday, Israeli aircraft attacked a building in the Jebaliya refugee camp next to Gaza City, killing a woman, a toddler and three young teenage girls, Gaza Health Ministry official Dr. Moaiya Hassanain said.

In the southern town of Rafah, a toddler and his two teenage brothers were killed in an airstrike aimed at a Hamas commander, Hassanain said. In Gaza City, another attack killed a man and his wife.

Gaza's nine hospitals were overwhelmed. Hassanain, who keeps a record for the Gaza Health Ministry, said over 1,400 were wounded over two days of fighting, and that casualties were now being taken to private clinics and even homes.

Abdel Hafez, a 55-year-old history teacher, waited outside a Gaza City bakery to buy bread, one of the few people visible outdoors. He said he was not a Hamas supporter, but believed the strikes would only increase support for the group. "Each strike, each drop of blood are giving Hamas more fuel to continue," he said.

Israeli leaders have said the operation might be long. "The goal of our current operation is to ... create a situation where Israeli civilians living in the south of the country no longer have to live in constant fear of a Hamas rocket attack," government spokesman Mark Regev said Monday.

Since Israel's withdrawal from Gaza in 2005 after a 38-year military occupation, Israeli forces have repeatedly returned to the territory to hunt militants firing rockets at Israeli towns. But it has shied away from retaking the entire strip for fear of getting bogged down in urban warfare.

The assault has sparked diplomatic fallout. Syria decided to suspend indirect peace talks with Israel, begun earlier this year. The U.N. Security Council called on both sides to halt the fighting and asked Israel to allow humanitarian supplies into Gaza. The prime minister of Turkey, one of the few Muslim countries to have relations with Israel, called the air assault a "crime against humanity," and French President Nicolas Sarkozy condemned "the provocations that led to this situation as well as the disproportionate use of force."

The carnage inflamed Arab and Muslim public opinion, setting off street protests in Arab communities in Israel and the West Bank, across the Arab world, and in some European cities.

Some of the protests turned violent. Israeli troops quelling a West Bank march Sunday killed one Palestinian and seriously wounded another.

On Monday, a Palestinian stabbed and wounded four Israelis in a West Bank settlement before he was shot and wounded. It was not immediately clear if the attack was directly connected to the events in Gaza.

The Associated Press contributed to this report.