The Israeli air force launched dozens of raids on the Gaza Strip overnight after massive rocket fire from the enclave pounded southern Israel, leaving 17 people injured, sources said Tuesday.
An Israeli army spokesman confirmed an air operation code-named Protective Edge had been launched, but did not give details.
Several houses were targeted in the raids on the southern Gaza Strip, notably in Khan Yunes, witnesses said.
Israel has "crossed a red line by attacking houses", warned the Ezzedine al-Qassam Brigades, the armed wing of the Islamist Hamas movement which has its stronghold in Gaza.
"If this policy does not stop we will respond by enlarging the radius of our targets to the point where the enemy will be surprised," it said in a statement.
The attacks left 17 people injured, including seven children and two women. Two of the injured are in serious condition, Palestinian medics said.
"About 50 objects were targeted including four houses of activists, rocket launch sites and infrastructure," the Israeli army spokesman said, adding that the operation aimed to hit Hamas and reduce the number of rockets fired at Israel.
Reinforcements were deployed near the Gaza Strip, so a ground attack can be launched if need be, he added.
More reinforcements would "be gradually mobilised in the next days".
"The air raids we have carried out are only one step. The operation is not limited in time."
The spokesman said Hamas had about 100,000 rockets, some of which could hit Tel Aviv.
On Tuesday schools and holiday camps in an area of 40 kilometres (30 miles) around Gaza were closed and residents were asked to avoid any rallies.
Hamas militants in Gaza on Monday fired dozens of rockets at Israel, triggering the response in a new escalation which threatened to spiral into another major confrontation.
It was the worst escalation in and around Gaza since November 2012, with tensions threatening to drag the region into a fresh confrontation as Israel sought to contain five days of violent clashes in Arab localities following the grisly murder of a Palestinian teenager by Jewish extremists.
The Israeli military said Monday more than 40 rockets had been fired at the south within a short period.
"A barrage of over 40 rockets was launched from the Gaza Strip in the past hour. Seven rockets were intercepted over the city of Ashdod and five rockets were intercepted over Netivot," an army statement said, indicating that some 30 rockets had hit inside Israel.
The Ezzedine al-Qassam Brigades claimed responsibility for the attacks.
"Al-Qassam fired dozens of rockets on Netivot and Ashkelon, Ashdod and Ofakim in response to the Zionist aggression," a statement said.
"Qassam rockets are a natural reaction to the Israeli crimes against our people," said Hamas spokesman Sami Abu Zuhri in a statement.
"We are not afraid of your threats and will not surrender to your conditions, we will respond to your crimes."
Shortly afterwards, Israeli warplanes hit more than 30 targets near the southern Gaza city of Rafah in an area close to the Israeli border which is riddled with tunnels, Palestinian witnesses and security sources told AFP.
Israel's Channel 1 television said the attacks came after the security cabinet gave the military a green light to "toughen the response to Hamas".
The channel also showed footage of dozens of tanks massing near the border with Gaza, preparing for a possible offensive against the enclave.
"With this barrage of rockets, Hamas has crossed the red line, and unfortunately it will pay for it," senior officials told the private Channel 10 television.
The rocket fire came several hours after Israel staged around 16 air strikes on targets across Gaza, following a night in which warplanes attacked 14 targets, killing at least three militants, one from Hamas and two from the Popular Resistance Committees (PRC).
"The Zionist enemy has opened the gates of hell on itself," the PRC said.
Another five Hamas militants died and one was critically injured when a tunnel collapsed near Rafah, with the armed wing blaming it on an Israeli air strike.
But the Israeli army denied hitting the area, with a spokesman describing it as a work accident by militants mishandling explosives.
The latest flare-up came a day after Israel arrested six Jewish extremists in connection with the killing of the Palestinian teenager, who was kidnapped and burnt to death in a suspected revenge crime after last month's abduction and murder of three Israeli youths in the West Bank.
During the investigation, three of the suspects admitted to the murder in which the victim was burned alive, an official close to the investigation told AFP.
The July 2 killing sparked five days of violent clashes in annexed east Jerusalem and in Arab towns across Israel, with police arresting hundreds of people.
"Three out of six suspects in custody have confessed to the murder and burning of Mohammed Abu Khder, and performed a re-enactment of the crime," the source said, speaking on condition of anonymity.
The killing has caused shock, outrage, and no small measure of shame in Israel.
"To take a young boy, to kill him, to burn him -- what for?" asked outgoing President Shimon Peres.