The attacks started Tuesday evening and went into Wednesday morning, but Israel's Iron Dome missile defense system shot down numerous rockets.
Calm returned to the Gaza Strip and nearby Israeli communities Wednesday after the exchange of fire on Tuesday that stretched into the night.
Late Tuesday a spokesman for Jihad said a ceasefire agreement had been reached to restore calm, though the Israeli army declined to comment on the claim.
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.
Shortly after he spoke, Israel's military began air strikes in Gaza.
The last war in 2014 was especially devastating, with over 2,000 Palestinians killed, including hundreds of civilians, and widespread damage inflicted on Gaza's infrastructure in 50 days of fighting.
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Israel and Egypt launched the joint blockade of the Gaza coast in 2007 after Hamas took control of the strip.
Israeli fire has killed more than 110 Palestinians, a lot of them during the Hamas-led protests, which climaxed on May 14.
One exploded in the yard of a kindergarten, damaging its walls and scattering the playground with debris and shrapnel, about an hour before it was scheduled to open for the day.
Separately, on Tuesday Islamist groups from Gaza fired dozens of mortars at Israel, leading to Israeli air strikes.
Civilians in the area surrounding the Gaza Strip were instructed to stay in close vicinity of shelters.
Israel said its snipers had opened fire on attackers or people attempting to infiltrate under cover of protests, but United Nations and human right officials have accused Israel of using disproportionate force.
Palestinians run for cover as sand and smoke rise following an Israeli airstrike on a Hamas post in the northern Gaza Strip.
Tuesday's violence followed weeks of deadly unrest along the border between Israel and the blockaded Palestinian enclave. Seventy-two people were killed on the Israeli side. Hamas had urged people to storm Israel's border.
The Gaza Strip has been under Israeli blockade for more than a decade, with Israel saying it is necessary to prevent Hamas from obtaining means to attack.