Another heavy clash was reported in Shajaiyeh, on Gaza City's eastern outskirts.
The Israeli military said three soldiers were killed and 24 others wounded Monday evening when an errant Israeli tank shell hit a building they had occupied outside Gaza City.
Their deaths brought to four the number of soldiers killed in the ground operation.
Israel said its forces had killed or wounded "dozens" of militants during the operation.
Hamas has released no casualty figures, but Palestinian medical officials said civilians account for about half the 125 deaths recorded since Saturday.
At least 550 Palestinians in Gaza have been reported killed in the last 11 days. About one-fourth of them are civilians, according to estimates by the United Nations.
In addition to the four Israeli deaths in Gaza, an Israeli soldier and three civilians have been killed by cross-border rocket fire. Monday's dead in Gaza included an unusually high number of children, including three siblings from one family and four from another.
Three adults were killed when a bomb hit a tent set up to receive mourners for a paramedic killed Sunday in an airstrike.
The violence overwhelmed Shifa Hospital, Gaza's biggest. Wounded were treated in hallways because beds were full.
A senior Israeli military official said the Gaza offensive was going according to plan but was "very complicated because there are a lot of tunnels, a lot of bunkers, a lot of booby traps."
"Hamas is using a lot of mortars and bombing our forces from a distance," the official said in a briefing for foreign correspondents. "They're [also] fighting us at short range . . . in houses, in buildings, in tunnels. They're exploiting every advantage because they know the place very well."
He said the army had captured dozens of militants and sent them to interrogation centers in Israel.
Hamas has given few accounts of the fighting. Its leaders are in hiding and make sporadic appearances on Hamas TV. One of them, Mahmoud Zahar, surfaced in a grainy video Monday, exhorting Palestinians to take revenge.
"The Zionists have legitimized the killing of their children by killing our children," he said.
Maj. Avital Leibovich, an Israeli military spokeswoman, said Hamas was to blame for civilian casualties because it operates in densely populated areas.
"Civilians will probably continue to get killed, unfortunately, because Hamas put them in the first lines of fire," she said.
