Gaza City, Gaza Strip - Israeli ground troops and tanks cut swaths through the Gaza Strip early Sunday, cutting the coastal territory into two and surrounding its biggest city as the new phase of a devastating offensive against Hamas militants gained momentum.

    The military used overwhelming firepower from tanks, artillery and aircraft to protect the advancing soldiers, and Gaza officials said at least 31 civilians were killed in the onslaught. The military said troops killed several dozen militants, but Gaza officials could confirm only four dead - in part because rescue teams could not reach the battle zones.

    The ground invasion and live images of the fighting in Gaza drew international condemnations and dominated news coverage on Arab satellite TV stations, many of which aired footage of wounded Palestinians at hospitals. Hamas threatened to turn Gaza into an Israeli "graveyard."

    Thousands of soldiers in three brigade-size formations pushed into Gaza after nightfall Saturday, beginning a long-awaited ground offensive against the area's Hamas rulers after a week of intense aerial bombardment. Black smoke billowed over Gaza City at first light as bursts of machine gun fire rang out.

    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.

    The new deaths brought the death toll in the Gaza Strip to more than 500 since Dec. 27. Palestinian and U.N. officials say at least 100 civilians are among the dead.

    TV footage showed Israeli troops with night-vision goggles and camouflage face paint marching in single file. Artillery barrages preceded their advance, and they moved through fields and orchards following bomb-sniffing dogs to guard against booby-traps.

    Gaza City's 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.

    She said no one slept overnight. "We keep hearing the sounds of airplanes and we don't know if we'll live until tomorrow or not," she said.

    Gaza health officials said the dead included a 12-year-old girl, five members of a single family, eight civilians killed by a tank shell in the northern Gaza town of Beit Lahiya, and an ambulance driver.

    The military reported 30 Israeli troops were wounded, two seriously, in the opening hours of the offensive.

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

    "This morning I can look every one you in the eyes and say the government did everything before deciding to go ahead with the operation. This operation was unavoidable," he said.

    A senior military officer said Hamas was well-prepared for the Israeli incursion into Gaza, a densely populated territory of 1.4 million where militants operate and easily hide in civilian the crowded urban landscape. He said the operation was "not a rapid one that would end in hours or a few days."

    Still, he said, "We have no intention of staying in the Gaza Strip for the long term." He spoke on condition of anonymity in accordance with army regulations.

    Israel says the objective is to restore quiet to Israel's south, not to topple Hamas or reoccupy Gaza.

    "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.

    At midafternoon, the Hamas Interior Ministry said it was still in control of Gaza and had captured residents collaborating with Israel, as well as traders exploiting the situation to inflate their prices. "The security forces are working, despite the shelling of its compounds ... It is protecting the back of the resistance," said ministry spokesman Ihab Ghussein.

    Rocket fire into Israel has persisted, and more than 30 rockets and mortar shells fell in Israel on Sunday morning, sending Israelis scrambling for bomb shelters. Two Israelis were lightly wounded. In much of southern Israel, school has been canceled and life has been largely paralyzed.

    While the air offensive presented little risk for Israel's army, sending in ground troops is a much more dangerous proposition. Hamas is believed to have some 20,000 gunmen and has had time to prepare. Israeli leaders had resisted a ground invasion for months, fearing heavy casualties.

    Israel has called up tens of thousands of reserve soldiers, which defense officials said 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 decide to launch attacks. Hezbollah opened a war against Israel in 2006 when it was in the midst of a large operation in Gaza.

    An armored force south of Gaza City penetrated as deep as the abandoned settlement of Netzarim, which Israel left along with other Israeli communities when it pulled out of Gaza in 2005, military officials and Palestinian witnesses said.

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

    The offensive focused on northern Gaza, where most of the rockets are fired into Israel, but at least one incursion was reported in the southern part of the strip. Hamas uses smuggling tunnels along the southern border with Egypt to bring in weapons.

    Ground forces had not entered major Gaza towns and cities by mid-day Sunday, instead fighting in rural communities and open areas militants often use to launch rockets and mortar rounds. But they took up positions on the outskirts of Gaza City and the nearby town of Jebaliya.

    Hamas was firing barrages of mortar shells toward Israeli positions. Israeli helicopter gunships are firing toward mortar launching sites.

    Israel launched the air campaign against Gaza on Dec. 27 with the aim of halting incessant rocket fire on its south. The operation appears to have slowed but not halted the rocket fire.

    Hundreds of rockets have hit Israel since the offensive began, and four Israelis have been killed. The relatively low number of Israeli casualties is largely due to warning sirens that give residents notice of incoming missiles and allow them to take cover.

    The death toll in Gaza has outraged many.

    U.N. Secretary General Ban Ki-moon conveyed his "extreme concern and disappointment" to Olmert and called for an "immediate end" to the operation.

    Denunciations also came from the French government, which unsuccessfully proposed a two-day truce earlier this week, and from Egypt, which brokered the six-month truce that broke down ahead of the Israeli offensive, as well as Turkey and Jordan, two other Muslim nations with ties with Israel.

    Palestinian President Mahmoud Abbas, a rival of Hamas who governs from the West Bank, condemned the Israeli invasion as "brutal aggression."

    The U.S. has put the blame squarely on Hamas. At an emergency consultation of the U.N. Security Council on Saturday night, the U.S. blocked approval of a statement demanded by Arab countries calling for an immediate cease-fire and expressing serious concern at the escalation of violence.

    Hamas emerged as Gaza's main power broker when it won Palestinian parliamentary elections three years ago. It has ruled the impoverished territory since seizing control from forces loyal to Abbas in June 2007.

    In the West Bank, Israeli troops shot and killed a 20-year-old Palestinian who was demonstrating against the Gaza offensive. The army said troops were quelling a violent demonstration and shot at the man when he tried to climb over Israel's West Bank separation barrier and ignored orders to stop.

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    Matti Friedman reported from Jerusalem.