There were no immediate reports of casualties from either side after more than 25 projectiles were launched from the Gaza Strip and the planes attacked three of the Iranian-backed armed group's facilities.
The Israeli military said most of the projectiles fired from Gaza were shot down by its Iron Dome rocket interceptor but one exploded in the yard of a kindergarten, damaging its walls, about an hour before it was scheduled to open for the day.
There was no claim of responsibility from any of the armed groups in Gaza, which is controlled by the Islamist terrorist Hamas movement, but the attack comes after Islamic Jihad vowed to take revenge after three of its members were killed by Israeli tank shelling.
Violence has soared along the Gaza frontier in recent weeks during which 116 Palestinians were killed by Israeli fire at mass demonstrations for a right of return to ancestral lands now in Israel.
Israeli Prime Minister Benjamin Netanyahu said the military would launch a forceful retaliation for the mortar attack, pointing the finger at Hamas and Islamic Jihad, which praised the barrage as a response to Israeli killings of Palestinians.
The air strikes occurred shortly after he spoke at a public event. Gaza residents identified the targets as Islamic Jihad training camps. The Israeli army said it was "carrying out activities in the Gaza Strip", without elaborating.
Nickolay Mladenov, the U.N.'s special coordinator for the Middle East peace process, said he was deeply concerned by "the indiscriminate firing of rockets by Palestinian terrorists from Gaza towards communities in southern Israel".
Calling for restraint by all parties, he said at least one of the mortar bombs "hit in the immediate vicinity of a kindergarten and could have killed or injured children".
Organisers of the Palestinian border protests launched a boat from Gaza on Tuesday in a challenge to Israel's maritime blockade of the enclave.
"I want to make a future for myself, I want to live," said Ehab Abu Armana, 28, before he and 14 other protesters boarded the boat. The Israeli navy was widely expected to stop the vessel, which the organisers said would be accompanied for a short distance by several other boats.
More than two million Palestinians are packed into the narrow coastal enclave. Israel withdrew its troops and settlers from Gaza in 2005 but, citing security concerns, maintains tight control of its land and sea borders, which has reduced its economy to a state of collapse.
Egypt also restricts movement in and out of Gaza on its border.
Peace talks between Israel and the Palestinians have been stalled since 2014 and Israeli settlements in occupied territory Palestinians seek for a state have expanded.
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