Several buildings were on fire, witnesses said, including a lumberyard. The sound battle could be heard clearly around the city of 400,000 as the Israeli forces, backed by artillery and attack helicopters, moved into neighborhoods east and south of Gaza City. Israeli gunboats shelled the coast from the west.

The Israeli military said it carried out some 60 airstrikes overnight, hitting groups of Hamas militants holed up in a hotel, a house and a mosque. It said it also struck 15 squads of gunmen, rocket launching sites and 15 smuggling tunnels along the Egyptian border.

The army said it had killed or wounded about 30 militants, and that three soldiers were wounded in overnight fighting. Among them was an officer who was seriously wounded when a bomb exploded in a northern Gaza house that he was searching. Weapons, including a machine gun, were later found in the house, the military said.

Dr. Moaiya Hassanain, a Palestinian Health Ministry official, said dozens of calls for ambulances had been received, but they could not be dispatched because of the fighting.

The Gaza fighting has raised tensions around the region and galvanized anger toward Israel throughout the Arab world. On Tuesday, at least one gunman opened fire at an Israeli army patrol along the desert border between Israel and Jordan, the military said. There were no casualties, and Jordan said the claim was "baseless."

There was a similar shooting on the Israel-Syria border on Sunday, and last week militants in Lebanon fired rockets into an Israeli town in an apparent attempt to draw Israel into a second front.

The Israeli military has tightly controlled information from the battlefield, but indications have been that Hamas has not put up a serious fight.

Of the nine Israeli soldiers killed during the offensive, four were killed in "friendly fire incidents," a military inquiry concluded. Repeated Hamas claims of spectacular attacks on the Israelis have turned out to be false.

Speaking in parliament on Tuesday, Israel's military chief said his troops have achieved a lot but "still have work to do" in fighting Hamas in Gaza.

"The soldiers are doing exceptional work, with many achievements in inflicting damage on Hamas, its infrastructure, its government and military wing," he said.

Diplomatic efforts to end more than two weeks of fighting have moved slowly, in part because of the wide gaps between Israel and Hamas.

Israel says it will push forward with the offensive until Hamas ends all rocket fire on southern Israel, and there are guarantees the Iranian-backed militant group will stop smuggling weapons into Gaza through the porous Egyptian border.

Hamas has said it will only observe a cease-fire if Israel withdraws from Gaza.