Targets included drone sheds, a rocket-making workshop and "army compounds", a army assertion mentioned.
In response to a question from Army Radio about Israel's relatively measured response to a barrage of mortar and rocket fire, Bennett said that Israel has to focus on the real culprit. No Israelis have been killed and only one soldier has been reported lightly wounded.
The airstrikes reportedly came in response to rockets fired into Israeli territory by Gaza militants.
Palestinian militants continued to fire additional barrages toward southern Israel, setting off air raid sirens in the area throughout the night.
The armed wings of Hamas and Islamic Jihad claimed responsibility for the firing, saying it was in response to Israel's killing of dozens of Palestinians since March 30, a lot of them in Gaza border protests.
Violence has soared along the Gaza frontier in recent weeks, during which 116 Palestinians were killed by Israeli fire at mass demonstrations calling for Palestinians' right to return to ancestral lands now in Israel. Sources told Ma'an that Israeli planes launched seven missiles targeting an al-Quds Brigades site, the military wing of the Islamic Jihad movement.
"The Israeli Navy apprehended a Palestinian boat with approximately 17 Palestinians that attempted to breach the legal naval blockade", the army said in a statement, saying the incident took place "without exceptional events".
Israel holds Hamas responsible for all violence emanating from the coastal enclave, as it has ruled Gaza since 2007.
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They peaked on May 14, when at least 61 Palestinians were killed in clashes as tens of thousands of Gazans protested the U.S. transfer of its embassy in Israel to the disputed city of Jerusalem the same day.
One mortar shell exploded near a kindergarten building, a military spokesman said, causing damage to the structure.
Lieutenant-Colonel Jonathan Conricus, a spokesman for the Israel Defense Forces (IDF), said the most extensive strikes from Gaza since the 2014 war also drew "the largest IDF retaliatory attack" since that conflict.
Soon after he spoke, Israel's military began air strikes in Gaza.
Islamic Jihad is the second most-powerful armed group in Gaza after Hamas, which runs the Palestinian enclave.
There were no reports of further attacks after Hamas announced early on Wednesday that it would cease fire if Israel did the same.
One main boat carrying around 20 people accompanied by a group of smaller ones departed from the fishermen's port in Gaza City.
But the protests appear to be fueled primarily by a desire to ease the blockade. Some of the Palestinian protesters hurled fire bombs, burned tires or tried to breach the fence, undermining Hamas' claims that the protests were entirely peaceful. Seventy-two people were killed on the Israeli side. It accuses Hamas of trying to carry out attacks under the cover of protests and using civilian demonstrators as human shields.