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 yesterday, 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 U.S. blocked approval of a U.N. Security Council statement Saturday night calling for an immediate cease-fire.

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 today 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.

Yesterday, Israeli soldiers fought primarily in open areas in the launching zones used by Gaza's militants to send rockets raining down on Israeli cities.

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.

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. The tally is based on figures from the U.N. and Palestinian health officials as well as a count by The Associated Press.

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.

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

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

French President Nicolas Sarkozy scheduled talks today 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.

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

"I think what the Israelis are doing is very important," Democratic Sen. Harry 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 cease-fire 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 cease-fire. It does not make any sense."

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 yesterday morning, sending residents scrambling for bomb shelters. Four Israelis were lightly wounded.