Israeli jets bombed targets across the Gaza Strip in the night to Thursday, after a missile struck the southern Israeli city of Beersheba for the first time in two years.
A military spokeswoman in Tel Aviv would not specify the number of sorties that began around midnight and ended at 5 am (0300 GMT) Thursday.
But she confirmed it was the most extensive bombing of targets since the three-week Gaza war in 2008-09.
Prime Minister Benjamin Netanyahu condemned the missile strike on Beersheba - the first to hit the city since the Gaza conflict - as an "escalation" of violence.
"I don't suggest anyone test Israel's determination," he said at a joint news conference in Jerusalem with visiting Polish Prime Minister Donald Tusk. "This is a thing that no country would accept."
Another cabinet minister warned Palestinian militants not to test Israel's "determination" to protect its residents, specifically mentioning the Gaza offensive, which Israel launched in 2008 after an upsurge in rocket fire from the strip on its southern communities.
Yossi Peled, a former Israeli army general who currently serves as a minister without a portfolio, said it would be "easy but irresponsible to react immediately from the gut" to the missile strike.
"Part of our effort - and this is difficult - is not to put the whole region in flames," he told Israel Radio. "I hope that everyone realizes that Israel's determination to defend its residents should not be put to the test."
He said the Gaza offensive "is a small sample of what we can do."
A Palestinian witness said Israel's overnight targets in Gaza included two training grounds belonging to the Qassam Brigades, the armed wing of the Islamist Hamas movement running the enclave, on the southern outskirts of Gaza City.
There were no immediate reports of injuries, but severe damage was reported.
Much of Gaza's population of 1.8 million was kept awake overnight by the noise of F-16 planes and Apache helicopter gunships flying overhead.
On Wednesday evening, a Russian-style Grad rocket had struck Beersheba, known as the capital of the Negev desert and home to some 200,000 people.
The missile hit the yard of a house. The occupants of the house escaped injury by hiding in a safe room, after a warning siren was sounded.
It was not immediately clear who was responsible for the attack, but it was believed to have been the armed wing of the Islamic Jihad. One of its militants had been killed in a fierce clash east of Gaza City with an Israeli border force earlier Wednesday. At least 11 Palestinians were injured in that clash.
An analyst in the daily newspaper Israel Hayom wrote that Israel found itself in a dilemma - on the one hand needing to keep up its "deterrence" and react harshly, so that Gaza militant factions would not be encouraged to fire more rockets at Israeli cities.
On the other hand, he said, Israel should not react too harshly as it could otherwise face the prospect of ordinary Arabs and their leaders uniting against it at a time of turmoil and instability in the Middle East.
