Fighting erupted at dawn on Wednesday when about 50 Israeli tanks and bulldozers drove into northern Gaza, flattening orchards and greenhouses to deprive militants firing rockets of cover, the army said.
Troops also took over rooftops of several houses, according to residents.
As the tanks moved forward, the military said aircraft attacked three groups of militants who were approaching the troops.
Gunfire was reported throughout the night and Hamas said it destroyed three army vehicles.
Israeli aircraft also blasted several houses, which the military believed belonged to Hamas and Islamic Jihad fighters, after warning people to leave via phone calls to those inside.
There are conflicting reports over how many of those killed were fighters and from which groups they came from, but at least six Hamas fighters were killed, along with at least one Islamic Jihad fighter.
The civilians killed included a three-year-old girl and a mentally handicapped young man, medical sources said.
"These numbers are going to multiply if we continue to be the forgotten zone in this region"
Saeb Erekat, Palestinian lawmaker
Dozens of Palestinians were also injured in the attacks, including a cameraman for the Palestine Broadcasting Corporation, who was hit in the back by shrapnel.
Israel launched its offensive into Gaza after Palestinian fighters launched a cross border raid on an Israeli army post on June 25, killing two Israeli soldiers and capturing two more.
"This is a horrible situation, and we urge the international community to notice the continuing Israeli escalation in Gaza immediately," Palestinian spokesman Saeb Erekat said.
"I'm afraid these numbers are going to multiply if we continue to be the forgotten zone in this region."