Palestinians and rights groups say unarmed protesters are being shot while posing no real threat.
The Israeli military said one airstrike had hit a high-rise building in al-Shati refugee camp in the northern Gaza Strip, describing the target as a Hamas urban warfare training facility with a tunnel underneath.
Hamas spokesman Fawzi Barhoum said the group was responsible for Saturday's barrage against Israel and that it was carried out "in response to the Israeli air strikes".
Israel's armed forces said dozens of strikes targeted military facilities belonging to the Gaza Strip's Islamist rulers Hamas, against which it has fought three wars over the past decade.
'We are not in a (military) operation.
Netanyahu said it was chose to take "powerful action against Hamas terror". Striking in the heart of Gaza City is typically only seen during full-blown conflicts like the 2014 war and could signal that a further escalation may be in store.
The airstrikes came after an Israeli soldier was wounded by a grenade during border protests on Friday and Gaza militants launched more than 200 rockets and mortars into Israel overnight Friday and through Saturday.
Israeli warplanes targeted an under-construction building in al-Katiba neighborhood in Gaza on Saturday, the Palestinian Health Ministry said.
Eight Boys Rescued From Thai Cave, Four More and Coach Still Trapped
Four more young footballers and their coach at the Mu Pa (WIld Boar) Academy Mae Sai , Ekkapol Chantawong, are still on the ledge. In a letter of his own, the coach , Ekapol Chanthawong, apologized to the boys' parents for the ordeal. "The water level is low".
"We were sitting in the living room and all of a sudden, the aquarium exploded and there was smoke everywhere and glass flew everywhere", said Aharon Buchris, who was wounded along with his wife and two teenage daughters, as he awaited surgery in hospital.
The projectiles are a combination of mortar shells and rockets, according to IDF spokesman Lt. Col. Jonathan Conricus. "We have no intention to harm anyone who is not a terrorist", he said.
There have also been hundreds of fires at Israeli farms caused by kites and balloons carrying firebombs from Gaza, leading to political pressure on the government and military to take action against Hamas. It said paramedics in the southern city of Sderot were treating a 52-year-old man with a chest wound, a 17-year-old girl with a face wound and a 20-year-old woman with injuries to her limbs.
Hamas has stopped short of claiming responsibility for the rocket fire but one official earlier called it a "deterrent to further Israeli attacks". "Bombardment for bombardment", he said.
The exchange of fire followed months of tension that has raised the prospect of a fourth war in the blockaded Gaza Strip since 2008.
With Israel focused on efforts to prevent Iran from establishing a permanent military foothold in neighboring Syria, it has been wary of escalating violence in Gaza. He didn't identify the mediators, but local media, quoting unidentified Hamas officials, said senior Egyptian intelligence officers and United Nations special envoy Nicolai Mladenov brokered the accord.
A Palestinian teenager killed in an Israeli air strike.
Palestinians in Gaza have been rallying every Friday since March 30 as a part of a peaceful campaign known as the Great March of Return.