Three Israelis were hurt by one of more than 90 rockets fired on Israel.
On Sunday, the Israel's military announced that the strikes on the east of Gaza were in response to mortar fire from the besieged enclave. There was no immediate comment from officials in Cairo.
A 15-year-old Palestinian who tried to climb over the fence into Israel was shot dead.
Such rocket attacks have become a regular feature of the asymmetric conflict between Hamas and Israel, driving the IDF to develop the Iron Dome defence system to intercept and destroy incoming rockets. Palestinian media said the IDF had shelled the home of a senior Islamic Jihad leader, but there was no confirmation from the army. One rocket landed inside a kibbutz in the Shar HaNegev Regional Council area. It is not known if the group was responsible for any of the rockets fired on Saturday.
"The action we are taking draws a clear red line: that from now on, we will not allow this".
The blasts shook homes and shattered windows, and black plumes of smoke rose from the sites of the explosions.
Qassem said that he had told the sides that Israel started launching the airstrikes on Gaza and it was the Israeli military that has to stop the strikes. The Israelis retaliated with live fire, killing a Palestinian teen and injuring 220 others throughout the day, Wafa reported.More news: Trump dishes up fresh dose of chaos aimed at May, Londoners
Gaza officials said 220 others were hurt in Friday's riots. Nearby houses were damaged.
"We are ready to operate simultaneously in different theaters", Conricus said, referring to the dual threats from Syria and Gaza.
"In the wake of events overnight we have attacked 40 terrorist targets, including the destruction of the headquarters of the Beit Lahia Battalion", said Chief IDF Spokesman Brig.Gen Ronen Manelis.
It said its jets targeted a Hamas tunnel in the southern portion of the Gaza Strip early on Saturday morning, alongside Hamas military compounds. "Bombardment for bombardment", he said.
Air raid sirens blared in southern Israeli communities as the fresh exchange of fire took place along the Israel-Gaza border. The initial wave of IDF strikes came in response to an incident Friday in which an Israeli officer sustained moderate injuries in a cross border grenade attack as well as ongoing arson attacks.
With Israel focused on rising tension along its northern border in its efforts to prevent Iran from establishing a permanent military foothold in post-civil war Syria, it has been wary of escalating hostilities in Gaza.
The IDF spokesman said the aim of the operation was to "restore a sense of security" and that the military would "respond as necessary" to a wide range of scenarios.
Gaza health officials say more than 130 Palestinians were killed and 15,000 others injured by Israeli forces during the protests.