GAZA CITY, Gaza Strip - Thousands of Israeli troops backed by tanks and helicopter gunships surrounded Gaza's largest city and fought militants at close range Sunday, the first full day of an overwhelming ground offensive in the coastal territory.

Israel said it has inflicted a heavy blow against Hamas as it expands a weeklong offensive meant to stop rocket fire on southern Israel. But spiraling civilian casualties among Palestinians fueled an international outcry, even as the US blocked approval of a UN Security Council statement Saturday night calling for an immediate ceasefire.

Israel's ground forces moved in after nightfall Saturday following hours of intense, fiery artillery shelling to clear the way, and Hamas warned that its fighters would turn Gaza into an Israeli "graveyard."

Palestinians reported clashes early Monday in eastern Gaza near the border with Israel. Hamas militants fired rocket-propelled grenades and mortars at advancing Israeli tanks. Explosions could be heard in Gaza City as aircraft attacked buildings. There was no immediate word about casualties.

On Sunday, Israeli soldiers fought primarily in open areas in the launching zones used by Gaza's militants to send rockets raining down on Israeli cities. As the troops in three brigade-size formations moved in, residents of those Israeli cities began cautiously emerging from bomb shelters in hopes that the rocket fire would taper off.

A Palestinian carries a child into the Shifa hospital in Gaza City, wounded during the Israeli army operation in Gaza, January 4, 2009. [Agencies]

Backing up the troops, mobile artillery units fired shells that exploded in veils of white smoke over Gaza's urban skyline. Tanks pushed south of Gaza City as deep as the abandoned settlement of Netzarim, which Israel left along with other communities when it pulled out of Gaza in 2005.

That effectively cut off Gaza City, the territory's largest population center with some 400,000 residents, from the rest of Gaza to the south.

Israel's military chief said Hamas fighters were trying to draw soldiers deeper into Gaza's sprawling, densely packed urban areas, where the military said militants were shielding themselves behind civilians.

"You entered like rats," Hamas spokesman Ismail Radwan told Israeli soldiers in a statement on Hamas' Al Aqsa TV. "Gaza will be a graveyard for you, God willing," he said.

Israeli forces have not yet entered urban areas, said Brig. Gen. Avi Benayahu, the chief army spokesman. He warned, however, that the operation was not a "school trip" and would be long and demanding.

The ground invasion risks turning into intense urban combat, with house-to-house fighting, sniper fire and booby-traps. Hamas is believed to have some 20,000 gunmen and has had time to prepare.

To guard against hidden explosives, Israel's ground forces moved through fields and orchards with bomb-sniffing dogs.

Since the ground assault began, 64 Palestinian civilians have been killed, said Dr. Moaiya Hassanain, a Health Ministry official. The new deaths brought the death toll in the Gaza Strip to more than 512 since Dec. 27.

Five Israelis have been killed since the offensive began. One soldier has been killed in the ground operation and about 40 were wounded, some of them in heavy exchanges of fire near the militant stronghold of Jebaliya, a town on Gaza City's northern outskirts, the army said. Heavy Israeli casualties could undermine what has so far been overwhelming public support for the operation.

At one hospital in the northern village of Beit Lahiya, medics carrying three injured children in their arms rushed them to treatment. One of the children had a blood-soaked bandage wrapped around his head and covering his eyes.

An Israeli shell also struck an ambulance in the town, killing a paramedic, said Marwan Abu Ras, a hospital administrator. The relief organization Oxfam, which said the ambulance belonged to a partner organization, al-Awda Hospital, confirmed the shelling.

An airstrike hit another ambulance belonging to the Hamas-run Health Ministry in Gaza City, killing three other paramedics, said medic Jamal Hawajiri. That ambulance crew was driving to a Hamas training site where there were reports of wounded.

An Israeli army spokesman said he had no information on the incidents.

The Israeli army said it had killed dozens of armed Hamas gunmen, but Gaza officials could confirm only a handful of dead fighters, in part because rescue teams could not reach the battle zones.

Condemnation of Israel's ground operation poured in from the Middle East and Europe.

Israeli armoured military vehicles move near Kibbutz Nahal Oz along the border with the Gaza Strip January 4, 2009. Israeli soldiers and Palestinian militants battled on Gaza City's outskirts on Sunday after Israeli troops and tanks invaded the coastal enclave in the worst fighting in the conflict in decades. [Agencies]

"The violence has to stop," said EU External Relations Commissioner Benita Ferrero-Waldner.

French President Nicolas Sarkozy scheduled talks Monday with Israeli and Palestinian leaders. While blaming Hamas for causing Palestinian suffering with rocket fire that led to the Israeli offensive, Sarkozy has condemned Israel's use of ground troops, reflecting general world opinion. Sarkozy and other diplomats making their way to the region are expected to press hard for a ceasefire.

Israel has four main demands: an end to Gaza rocket fire, a halt to Palestinian attacks, international supervision of a truce and an agreement to stop Hamas from re-arming. Hamas demands a cessation of Israeli attacks and opening of vital Gaza-Israel cargo crossings, Gaza's main lifeline.

US officials maintained their firm support for Israel and squarely blamed Hamas.

Vice President Dick Cheney said Israel "didn't seek clearance or approval from us" before pushing into Gaza.

Sens. Harry Reid and Dick Durbin, the top two Democrats in the chamber, and Senate Republican leader Mitch McConnell all described Israel's actions as understandable.

"I think what the Israelis are doing is very important," Reid said. "I think this terrorist organization, Hamas, has got to be put away. They've got to come to their senses."

Israeli President Shimon Peres said that Israel had to push forward and that a ceasefire was pointless without a halt to Hamas rocket fire.

"Well, clearly, if there is somebody (who) can stop terror with a different strategy, we shall accept it," he said on ABC's "This Week."

"We shall not accept the idea that Hamas will continue to fire and we shall declare a ceasefire. It does not make any sense."

Palestinians said the Israeli military broke into broadcasts on the Hamas TV channel, Al Aqsa, appealing to Palestinians not to agree to serve as human shields for the militants. The message read, "Israel is acting only against Hamas and has no interest in harming you."

The ground operation is the second phase in an offensive that began as a weeklong aerial onslaught aimed at halting Hamas rocket fire that has reached deeper and deeper into Israel, threatening major cities and one-eighth of Israel's population of 7 million.

More than 45 rockets and mortar shells fell in Israel on Sunday morning, sending residents scrambling for bomb shelters. Four Israelis were lightly wounded.

In Gaza City, civilians cowered inside as battles raged, while terrified residents in other areas fled in fear. In the southern town of Rafah, one man loaded a donkey cart with mattresses and blankets preparing to flee.

Lubna Karam, 28, said she and the other nine members of her family spent the night huddled in the hallway of their Gaza City home. The windows of the house were blown out days earlier in an Israeli airstrike, and the family has been without electricity for a week, surviving without heat and eating cold food.

"We keep hearing the sounds of airplanes and we don't know if we'll live until tomorrow or not," she said.

Severe damage to Gaza's phone network was pushing the territory closer to complete isolation. The Palestinian phone company Paltel Group said 90 percent of Gaza's cellular service was down, as well as many landlines, because of frequent power cuts and the inability of technicians to reach work sites.

In his first public comments on the operation, Israeli Prime Minister Ehud Olmert told his Cabinet Sunday that Israel could not allow its civilians to continue to be targeted by rockets from Gaza.

"This operation was unavoidable," he said.

Military intelligence chief Maj. Gen. Amos Yadlin told the Cabinet Hamas was using mosques, public institutions and private houses as ammunition stores, Cabinet secretary Oved Yehezkel told reporters.

Israel approved the mobilization of thousands more reservists in addition to tens of thousands called up on Saturday. Defense officials said the extra forces could enable a far broader ground offensive.

The troops could also be used in the event Palestinian militants in the West Bank or Hezbollah guerrillas in Lebanon launch attacks, as Hezbollah did in 2006 when Israel was in the midst of a large operation in Gaza.