Israeli Prime Minister Ehud Olmert has said a Palestinian rocket attack on the Israeli city of Ashkelon marked a "major escalation" in Hamas's warfare.
Warning of "far-reaching consequences", Mr Olmert said "the Hamas organisation will be the first to feel this".
Israel's military meanwhile pressed on with its week-old offensive to free a captured soldier held in Gaza.
Israeli aircraft struck the Palestinian interior ministry headquarters in Gaza City overnight.
At least four people were injured in the attack which was the second strike on the ministry in a week.
Witness reported the complex was badly damaged. Nearby apartments were also hit, Reuters news agency reported.
Mr Olmert's warning came as the attack on Ashkelon struck an empty school in the deepest rocket strike inside Israel yet.
The Qassam rocket landed in a car park in the high school in central Ashkelon shortly after 1900 (1600 GMT) on Tuesday.
Pupils were on holiday and there were no injuries, although the rocket caused some damage and left a hole in the ground.
The BBC's Nick Thorpe in Jerusalem says the attack is being taken very seriously by Israel.
While Qassams regularly strike another Israeli town, Sderot, Ashkelon is further away from Gaza - some 10km (six miles) - and has been spared direct hits until now.
Mr Olmert called the attack "a major escalation in the war of terror that the Hamas organisation is responsible for".
A large Israeli force has been waiting on the northern edge of the Gaza strip for days, following Cpl Shalit's capture.
A small force entered the area on Monday morning and a larger force might now be sent in, to try to prevent more rockets being fired, our correspondent says.
The rocket attack came as Israel pressed on with its week-old campaign to free Cpl Gilad Shalit, believed to be held in southern Gaza.
Despite the expiry of the deadline set by the militants for Israel to free Palestinian prisoners, Israel said the 19-year-old tank gunner was alive.
SOLDIER CAPTURE TIMELINE
Sun 25 June: Cpl Shalit captured in cross-border attack
Mon 26 June: Captors propose prisoner exchange
Weds 28 June: Israel enters southern Gaza after air strikes
Thurs 29 June: Israel detains dozens of Hamas officials
Sat 1 July: Captors demand 1,000 prisoners be released
Mon 3 July: Captors issue deadline of 0300 4 July
Tues 4 July: Israel says Shalit still alive
"We know that until now Gilad Shalit is alive, we know that he is injured, that he was seen by a Palestinian doctor a few days ago," government spokesman Avi Pazner told French television.
But Abu al-Muthana, from the Islamic Army - one of three groups holding Cpl Shalit - said there would be no more talks nor information released about the soldier's fate.
As the crisis wore on, Mr Olmert warned that the fight against Palestinian militants would be drawn out.
"This is a long war. It requires lots of patience, sometimes endless restraint. We have to know when to clench our teeth and to deal a decisive blow.
The Hamas Prime Minister Ismail Haniya, whose Gaza offices were hit in a symbolic Israeli missile strike three days ago, appealed on Tuesday for Cpl Shalit's life to be spared.
"The government... is still calling for preserving the life of the captured Israeli soldier and for him to receive good treatment," Mr Haniya said.
The BBC's Middle East editor Jeremy Bowen says nobody on either side knows how long this crisis will last.
Their public statements are a form of psychological warfare, to show resolution and to put pressure on their opponents, he says.