There were no reports of Palestinian casualties in the Israeli strikes.
By late Tuesday, Israeli aircraft had hit 55 facilities belonging to militant groups in Gaza, including a cross-border tunnel under construction, in response to the Palestinian barrages, the military said.
Hamas and Islamic Jihad also started to evacuate military bases and installations across Gaza in anticipation of the Israeli retaliation.
Hamas seized control of the Gaza Strip in 2007.
An Israeli tank drives along the border with the Gaza strip, on the Israel-Gaza border, May 29, 2018.
"Bombardment for bombardment and blood for blood".
In technical terms, there is an ongoing ceasefire between Israel and Hamas as a result of Operation Protective Edge, which took place during the summer of 2014.
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By Wednesday morning, however, there was some indication of a cease-fire between the sides amid several hours of quiet, though it was unclear if it would hold.
Whilst a senior Israeli official said Israel was not interested in war but would respond "forcefully" to any rocket fire from the Strip, the Times of Israel reported.
Egypt was said to have performed a significant role in stopping violence in Gaza from sliding into full-blown military conflagration during the last escalation on the border.
Israeli Prime Minister Benjamin Netanyahu said his army would react "forcefully" to the dozens of mortars fired at Israel.
Israeli soldiers stand guard next to an Israeli Iron Dome defence system, created to intercept and destroy incoming short-range rockets and artillery shells, deployed along the fence with the Gaza strip on May 29, 2018. One exploded in the yard of a kindergarten before it was due to open.
The mortar fire yesterday which sparked this round of hostilities between Hamas and Israel came at then of multiple weeks of riots and attempted infiltrations from Gaza into Israel.
The attacks on Tuesday sent Israeli civilians running to bomb shelters as air raid sirens wailed.
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"Palestinian Islamic Jihad is a pure Iranian proxy and a very militant organization".
Israeli Defense Minister Avigdor Lieberman commented the issue, saying the strikes against Gaza are "only the beginning".
No one was injured in the incident, Steinitz said.
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 militants from Gaza towards communities in southern Israel".
Israel says the blockade is needed to prevent Hamas from building up its military capabilities. "The resistance factions will abide by it as long as the Occupation [the group's reference to Israel] does the same".
The flare-up comes amid ongoing tensions along the Gaza border, with more than 110 Palestinians killed by Israeli forces there in recent weeks.
After a day that saw an vast barrage of rockets and mortars fired at Israelfrom terrorists in the Gaza Strip, red alert sirens have continued late into the night, forcing tens of thousands of Israelis to sleep in protective shelters.
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