The Islamic Jihad group, a militant faction operating in the Hamas-ruled Gaza but that has close ties to Iran and Syria, said they agreed to Egyptian mediation efforts and halted the rocket fire, the heaviest to emanate from Gaza in months.
Following the exchanges, Islamic Jihad's media office announced on Saturday morning that it had accepted an Egypt-mediated ceasefire with Israel.
The Islamic Jihad movement, which was founded in the late 1970s, is much smaller than Hamas and maintains that Palestine, with its borders marked from the Jordan river to the Mediterranean sea, is Islamic land and it is religiously prohibited to compromise or surrender any of it.
Israeli military spokesman Lieutenant-Colonel Jonathan Conricus accused Syria and Iran of involvement in the attack. "We know that the orders, incentives were given from Damascus with the clear involvement of the Iranian Revolutionary Guard Quds Force".
Israel says the decade-long blockade is necessary to isolate Hamas, while critics say it amounts to collective punishment of Gaza's two million residents.
Israeli aircraft have struck dozens of militant sites across the Gaza Strip as militants fired some 30 rockets into Israel.
The sides have fought three wars since Hamas seized control of Gaza in 2007.
The Israeli military said it had struck two arms workshops, five bases, a training camp, an entrance to an underground tunnel and an observation post among other targets.
On Sunday, Israel reopened the people and goods border crossings with Gaza and on Wednesday renewed the flow of Qatar-funded fuel to the Palestinian enclave, in an indication of its confidence that Hamas would rein in violence.
After deadly protests, rockets fly and Israel strikes Gaza
Israel has bombed dozens of targets in Gaza after being hit by rockets from the region.
Sources also confirmed that the rockets fired from Gaza landed in open fields in Israel. Hamas wants the deal to end a crippling Israeli-Egyptian blockade on Gaza.
Five Palestinians were shot dead by Israeli fire in separate incidents along the border fence, the Gaza health ministry said. An Israeli soldier was killed by a Palestinian sniper.
The largest projectile attacks in months which continued into Saturday and border fatalities came despite talk of progress towards an Egyptian-brokered deal to end the months of often violent protests along the border.
The bombing destroyed a site near the Indonesian hospital in the northern Gaza Strip, damaging the medical centre, the Ministry of Health said.
Israel accuses Hamas of using the large protests as cover to stage border infiltrations and attacks.
Palestinians have gathered for protests along the border at least weekly since March 30.
Thousands of Palestinian demonstrators have come out for 31 weeks to denounce the blockade of the Gaza Strip and call for the right of return of Palestinian refugees to the homes, from which they and their families were displaced during the establishment of the state of Israel. A Gaza militant fatally shot an Israeli soldier in July.
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Net sales at the West's e-commerce leader climbed to $56.6 billion in the third quarter, up 29 percent year-on-year. Alphabet shares lost ground after the earnings report and were down 5.04 percent in pre-market trading Friday.