The groups said Egyptian mediation efforts had succeeded in brokering a truce ending an intense daylong round of violence, the Associated Press reported.
"In consultation with the minister of defence, the chief of staff and the top security command of the state of Israel, we have decided on strong action against Hamas terrorism", Mr Netanyahu said in a video statement.
The raids were a response to rockets fired into Israel, he said.
An Israeli military spokesman declined to comment, but said its actions would depend on what happens on the ground.
Israel said it carried out the airstrike after Hamas fired dozens of rockets into Israel throughout the day, threatening to trigger an all-out war after weeks of growing tensions along the volatile border.
Gaza health officials say more than 130 Palestinians were killed and 15,000 others injured by Israeli forces during the protests.
The Israeli army said air strikes carried out in the morning hit "complexes used to prepare arson terror attacks and a Hamas terror training facility".
Two Palestinian teenagers were killed in an airstrike in Gaza City, while three Israelis were wounded from a rocket that landed on a residential home.
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"We are talking about the biggest offensive strikes since Protective Edge", Brigadier General Tzvika Haimovic told journalists, referring to Israel's name for its 2014 operation in the Gaza Strip.
Sirens wailed overnight and throughout most of the day Saturday in southern Israel as waves of rockets and mortars were launched from Gaza amid the airstrikes. Israel's Iron Dome rocket interceptor system often shoots down Gaza projectiles.
According to the IDF, a military officer was lightly wounded by a grenade thrown at the border on Friday.
The Gaza health ministry said 15-year-old Othman Rami Halles was killed east of Gaza City.
Israelis living in nearby communities were ordered by the IDF to bring their children indoors and to close their windows due to the necessity of using tear gas to disperse the thousands of violent Gazans attempting to breach the security fence at the border.
Rocket warning sirens went off in the Israeli coastal city of Ashkelon, about 12 km (7 miles) from the enclave, further north than in recent attacks. Fourteen others were wounded.
The army earlier on Saturday said it targeted two Hamas attack tunnels as well as other military compounds in the Strip, including those involved in the spate of incendiary kite and balloon attacks.
In retaliation, Israel on Monday announced the closure of Gaza's main commercial border terminal, reduced the area Palestinian fishing boats are allowed to operate off Gaza's Mediterranean coast and blacklisted what it described as a pro-Hamas TV channel.
Israel says Hamas has been orchestrating the weekly protests to distract from governance problems and provide cover for militants' cross-border attacks.