Thirty Hamas rockets were fired on Israel from the Gaza Strip Tuesday night and early Wednesday morning.
In total, 18 rockets were fired towards Israeli territory in a number of separate incidents, the army said.
The military says the country's Iron Dome anti-missile shield intercepted seven rockets.
Read the full story. Over 100 Palestinians have been killed by Israeli fire since they began.
The IDF believes that extremist elements in Hamas' military wing are mistaken in their assessment not only of the IDF's readiness, but also of the readiness of the Israeli political echelon to launch this large-scale operation in the Gaza Strip that would be as destructive as the 2014 Operation Protective Edge and yield more radical results. But support has come from its main ally, the United States, which like Israel, has cast blame on Hamas. Fighter jets targeted about 25 Hamas targets overnight in response to the heavy Palestinian fire, it said.
On Sunday, the IDF pounded Hamas targets in the enclave following numerous arson attacks the day before, warning that it had the "intelligence knowledge and operational capability" to conduct additional strikes if the balloon and kite attacks continued.
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Israel's tactics in confronting the weekly Friday protests have drawn worldwide condemnation.
"The IDF is prepared to continue operating with increased intensity and with various means in response to these terror attacks", an IDF representative said.
The protests are aimed in part at drawing attention to the decade-long Israeli-Egyptian blockade on the territory imposed after Hamas, a group sworn to Israel's destruction, seized control of Gaza.
Wednesday's rocket barrage was the second instance of rocket fire along the border in two weeks, after three rockets fired at Israel on Monday broke an implicit ceasefire that followed a sudden conflagration in late May.
Israeli forces have killed more than 120 Palestinians and wounded more than 3,800 during mass demonstrations along the Gaza border since March 30.
The Gaza Strip is controlled by the Islamist movement Hamas which Israel considers its chief enemy.