Israel's prime minister ordered the army on Wednesday to expand an offensive against the ruling Palestinian movement Hamas after its armed wing fired a missile from Gaza into a major Israeli city for the first time.
Political sources said Ehud Olmert, who launched the operation last week after a soldier was seized by Hamas gunmen and other militants, was also considering establishing a buffer zone in northern Gaza to halt the cross-border rocket fire.
An Olmert spokesman said no such decision had been taken on a move that could amount to re-occupying parts of the strip.
Hamas' armed wing hit the coastal city of Ashkelon on Tuesday with an upgraded home-made rocket that travelled 12 km (7 miles) from Gaza. No one was hurt but Olmert called it an "escalation without precedent".
"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.
In fresh violence, Hamas gunmen skirmished with Israeli troops and tanks that moved into parts of the northern Gaza border town of Beit Hanoun, witnesses said.
Militants said they fired at least two anti-tank rockets, hitting a tank and an armoured bulldozer. An army spokesman said one rocket-propelled grenade was fired at the vehicles.
One Beit Hanoun official said Israeli forces had also taken over some houses while hundreds of residents were forced to stay in their homes. The Israeli army said it was checking the report. There were no immediate reports of casualties.
The statement from Olmert's office said his security cabinet had approved strikes against the Hamas Islamists in Gaza and also the occupied West Bank, focusing on "institutions and infrastructure facilitating terrorism".
It also approved stepped-up attacks on rocket crews in Gaza. Israel quit Gaza last year after 38 years of occupation, but launched its offensive following the abduction of Corporal Gilad Shalit in a cross-border raid from Gaza on June 25.
The army has stopped short of a major push into northern Gaza towns. It entered the south last week, establishing a position in Gaza's disused international airport.
Israel has also detained eight Hamas cabinet members and nearly two dozen lawmakers in the West Bank. But the government has sought to play down concerns the army would get bogged down in Gaza.
The upgraded Hamas rocket, powered by two engines instead of the usual single motor, hit a schoolyard in the centre of Ashkelon, a city of 115,000 and the site of a major power plant. It was the first time a major Israeli city had been hit and provoked a media frenzy in Israel.