Explosions and heavy machine-gun fire have rocked Gaza City in the heaviest fighting yet of Israel's campaign to halt rocket attacks by Hamas.
On Monday, Israeli tanks and helicopters launched a night-time offensive that left three Israelis dead from friendly fire.
The Israeli army said three soldiers from the elite Golani Brigade were killed and 24 wounded when their position was accidentally hit by Israeli tank fire.
Flares lit up the skies over the Shejaiya district of the city as helicopters gunships targeted dozens of Hamas fighters with heavy machine guns, residents said.
All of Gaza City and the rest of the northern Gaza Strip have been without electricity.
On Tuesday, firing from Israeli naval ships killed 10 Palestinians in Deir al-Balah in the central Gaza Strip, say medical workers.
Witnesses say Israeli ships fired shells towards a beach in the area.
Hamas said of the fighting in Shejaiya: "The resistance drew Israeli forces into a trap and wounded seven. We have left a lot of explosives in their path."
Spokesman Abu Ahmed said the group had lost one man in the fighting. "A Jihad unit is taking part in the clashes with Israeli soldiers in eastern Gaza. They attacked the rear lines" of the Israeli forces.
"Communications with our fighters are cut at the moment but it is still going on," he said, adding that one fighter was killed in Shejaiya.
In the Bureij refugee camp, in the centre of the enclave, three people were killed by tank fire, medics said.
Witnesses said tanks continued to fire on the camp into the pre-dawn hours, but there was no indication that troops had entered it.
In the southern town of Rafah, on the Egyptian border, witnesses said an elderly woman was killed by an Israeli air strike.
Israeli artillery pounded Palestinian positions in Shejaiya and Zeitun before the attacks there started, and an army source said the fighting was extremely fierce.
Hamas said on Monday that it had thousands of fighters waiting in Gaza for the Israelis.
Israel launched an air offensive on Gaza on 27 December aimed, and on Saturday sent in thousands of soldiers.
Said Hamas: "We have prepared thousands of brave fighters who are waiting for you in each corner of the street and will welcome you with fire and iron."
At least 555 people have been killed in Gaza since 27 December and another 2,700 wounded. Of at least 60 Palestinians who died on Monday, 13 were children.