An Israeli army spokesman on Tuesday 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 Hamas resistance 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.
Reinforcements were deployed near the Gaza Strip, so a ground attack can be launched if need be, he added.
More reinforcements would "be gradually mobilized in the next days".
On Tuesday schools and holiday camps in an area of 40 kilometers (30 miles) around Gaza were closed and residents were asked to avoid any rallies.
The latest Palestinian 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 resistance fighters, 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 members died and one was critically injured when a tunnel collapsed near Rafah, with the armed wing blaming it on an Israeli air strike.
The latest flare-up came a day after Israel arrested six Israeli 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 the occupied East al-Quds and in Arab towns across the occupied land, with police arresting hundreds of people.
BA/BA