Palestinian medics said an Israeli tank shell killed five and an air raid killed two fighters on Wednesday.
The Israeli army said both hits were from air strikes, not tank shells, and said the latest attack in the town of Jabalya was against a group of militants who had fired an anti-tank missile at them.
Palestinian witnesses said the army fired on a crowd of Palestinians that had gathered to watch Israeli forces in the area.
They said three fighters from a Hamas-led security force were among the five killed in the second strike but did not say whether they had attacked the Israeli troops.
Twenty-three people were hurt, including 11 in critical condition, said Dr Joma Saka, a spokesman for Gaza City's Shifa hospital.
The fighting began before dawn when about 50 Israeli tanks and bulldozers entered northern Gaza, near the border with Israel, flattening orchards and greenhouses. Troops also took over rooftops of several houses, residents said.
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.
Homeowners said they received phone calls from people in broken Arabic telling them to get out.
Israel launched its offensive after Hamas fighters tunnelled under the border on June 25 and attacked an Israeli army post at a Gaza crossing, killing two soldiers and capturing a third.
Israeli ground forces have raided several parts of Gaza, as artillery pounds the area and aircraft fire missiles.