The Gaza offensive, which Israel says is aimed at recovering a captured soldier and stopping armed groups from firing makeshift rockets, has piled pressure on the Palestinian government led by Hamas, which demands a prisoner swap for the Israeli corporal.
Israeli tanks and armoured personnel carriers, backed by helicopters, moved into farmland near Beit Hanoun, an area often used by militants for launching rockets.
Small groups of fighters opened fire at the Israeli forces, but there was no report of casualties.
"There is an army activity in Beit Hanoun. There has been deterrent fire," one Israeli military source said.
Israeli troops had pulled out of the northern Gaza Strip a week earlier after a large raid into the territory, which Israel had abandoned last year after a 38-year occupation.
Israel killed two Palestinians and attacked the economy ministry on Saturday, striking at the Hamas administration. Israel holds Hamas responsible for the fate of Corporal Gilad Shalit, who was captured in a raid from Gaza on June 25.
Israel has said it will not discuss a prisoner exchange.
The Israeli offensive in Gaza has killed about 85 people, about half of them civilians.