Thousands of Israeli troops, backed by tanks and helicopter gunships, pushed deeper into Gaza Sunday, fighting militants at close range and surrounding the coastal territory's largest city in the first full day of an overwhelming ground offensive.

Israel said it has inflicted a heavy blow against Hamas as it expands a weeklong offensive meant to stop rocket fire on southern Israel. Still smarting from an indecisive offensive in Lebanon in 2006, the Israeli army has already reported at least one soldier killed and more than 40 injured in the ground campaign.

International outcry has ratcheted up as the Palestinian death toll in the Gaza Strip rose to more than 512 since December 27, with varying estimations from Gazan and independent sources putting civilian casualties between 20-25 per cent of that figure.

Gaza officials have said at least 31 civilians were among the dead since Saturday's incursion.

Moved in after nightfall

Israel's ground forces moved in after nightfall Saturday following hours of intense, fiery artillery shelling to clear the way.

On Sunday, Israeli soldiers continued to fight 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 emerging from bomb shelters in hopes that the rocket fire would taper off.

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

The Israeli military could face tougher pressure if Hamas fighters draw soldiers deeper into Gaza's sprawling, densely packed urban areas, where house-to-house clashes could further jeopardise civilians. Hamas has pledged that it would turn Gaza into a graveyard for the Israeli army. The militants are believed to have some 20,000 gunmen.

Two ambulances hit

Israeli gunfire hit two ambulances in Gaza, killing four paramedics.

Condemnation of Israel's ground operation poured in from around the Middle East and Europe, but the United States blocked approval of a United Nations Security Council statement Saturday night calling for an immediate ceasefire and expressing serious concern at the escalation of violence.