Palestinian officials and witnesses said at least seven tanks, along with armoured personnel carriers, entered the abandoned settlement of Nissanit, one of Israel's former settlements in northern Gaza, on Wednesday night.
Troops were reported to have earlier taken control of several houses in Bait Hanoun and skirmished with Hamas fighters.
Israel's cabinet had decided on Wednesday to send the military, which had been carrying out small operations in northern Gaza, deeper into the territory to prevent rocket attacks on southern Israel.
The movement by Israeli forces into Nissanit appeared to be part of that new offensive.
An Israeli military spokeswoman denied tanks had been moved to the former settlement sites in Gaza, but said some armoured vehicles were protecting troops in Bait Hanoun.
Five Israeli tanks and armoured vehicles were seen making their way very slowly into the old settlement while two other tanks took up positions atop a nearby hill as bulldozers built sand embankments around them.
On Wednesday, one person was injured by a Palestinian rocket that hit Ashkelon, the Zaka service said.
An earlier rocket fired by Hamas hit a vacant schoolyard. There were no casualties in that attack, but it was the first time that a makeshift rocket had reached so far and threatened a large Israeli population centre.
The Israeli security cabinet on Wednesday discussed establishing a buffer zone in northern Gaza.
A spokesman for Ehud Olmert, the prime minister, denied that the cabinet had approved the formation of such a zone, but officials said ministers had agreed that a standing plan by the army to form a buffer zone could be an effective way to prevent rocket fire.
"Given the abduction and continued ballistic salvoes, including the [rocket] launched at Ashkelon, the rules of the game in dealing with the Palestinian Authority and Hamas must be changed," a statement from Olmert's office said.
The statement from Olmert's office said his security cabinet had approved strikes against Hamas Islamists in Gaza and also the occupied West Bank, and also approved stepped-up attacks on rocket crews in Gaza.
The move indicates that Israel may be prepared to reoccupy part of Gaza, less than a year after withdrawing all its troops and settlements from the area.
The army was ordered to "prepare for a phased and continuous" operation as it continues to seek Corporal Gilad Shalit, 19, who was seized in a cross-border Palestinian raid on June 25.
Meanwhile, in another development, Aljazeera's correspondent in Gaza reported the number of Palestinians stranded on the Egyptian side of Rafah crossing had risen to more than 5000 Palestinians who were on their way back to their homes in the Gaza Strip.
Some Palestinians say that the situation is increasingly difficult for citizens, particularly those who were coming back after undergoing medical treatment in Egypt, along with children and the elderly.
The Israeli troops had earlier seized the crossing and shut it down 10 days ago.
Güncelleme Tarihi: 20 Eylül 2018, 18:16