Israeli forces have moved back into the northern Gaza Strip, a week after withdrawing during an operation to recover a captured soldier.
Israeli forces struck the Palestinian economy ministry on Saturday
Troops and tanks, backed by helicopters, moved towards the town of Beit Hanoun early on Sunday.
Three were killed and eight wounded by an Israeli air strike, Palestinian medical sources said.
Israeli forces have been attacking targets in Gaza for nearly three weeks since the capture of Cpl Gilad Shalit.
Israeli troops are also involved in attacks inside Lebanon after Hezbollah guerrillas there captured two more Israeli soldiers.
Beit Hanoun is an area often used by militants for launching rockets into Israel.
Small groups of militants exchanged fire with the advancing Israeli forces. The Israeli town of Sderot is a frequent target for Palestinian rockets.
Israel's declared goal is the return of Cpl Shalit and an end to the rocket fire.
Its forces withdrew from the northern Gaza Strip a week ago after completing its first operation. Forces then entered the southern Gaza Strip but before Sunday's incursion all ground forces had left.
Air strikes have continued throughout, however.
On Saturday, an Israeli air strike on a house in Gaza City killed one person and injured several, including young children, Palestinian sources said.
Israel said Hamas militants used the building as an ammunition depot and were preparing rockets there.
A second Palestinian died in northern Gaza under helicopter fire.
The economy ministry of the Hamas-led Palestinian government was also hit by air strikes and badly damaged but there were no reports of casualties.