There were reports of gunfire near the Maghazi Refugee Camp, not far from the Gaza Strip’s border and Palestinian officials said a Hamas militant was seriously wounded.
Israel has been pursuing an offensive in the Gaza Strip to try to recover a soldier, who was captured in a raid by Palestinian militants on June 25, and to halt rocket fire over the border.
At least 85 Palestinians have been killed since the offensive began.
The Israeli tanks moved into the refugee camp under cover of machine-gun fire from troops.
The camp, with 22,000 residents, is near the Gaza-Israel fence, opposite the Palestinian town of Deir al-Balah.
Israeli forces operated in the region late last week before withdrawing.
Israeli troops have also swept through southern Gaza and carried out two invasions of northern Gaza, trying to stop militants from firing rockets at Israel.
The move into Mughazi was preceded by several hours of tank movements on the Israeli side, as well as exchanges of fire between soldiers and Palestinian gunmen.
Israel began a large operation in Gaza on June 28, three days after Hamas linked militants tunnelled under the border and attacked an Israeli army base at a Gaza crossing, killing two soldiers and capturing a third.
A team of United Nations envoys has met with Palestinian President Mahmoud Abbas in Gaza City about the Israeli offensive in the territory.
“We hope the present crisis engulfing Gaza is to be overcome and we can come back to the situation where it is possible to pursue the objective of peace,” UN envoy Alvaro De Soto said after the meeting.
Palestinian officials said the UN team brought no offers of a deal to end the fighting to Mr Abbas, who called for an immediate ceasefire.
In a statement, the Israeli military said it opened two crossings into Gaza on Tuesday to allow shipments of food and fuel.
About 145 food trucks entered Gaza through the Karni crossing, while 500,000 litres of diesel fuel, 90,000 litres of petrol and 175 tonnes of cooking gas were sent through the Nahal Oz crossing.