Israeli sirens warning of imminent rocket and mortar strikes sounded late into the night and Israeli aircraft hit 55 militant targets in the Gaza Strip, including a cross-border tunnel under construction, the military said. Daoud Shehab, an Islamic Jihad spokesman, also said an Egyptian official had been in contact with the group to try to restore calm.
"Hamas again chooses to act against the interests of the residents of the Gaza Strip and, after failing to improve the social order, and instead encouraging violence along the security fence, chooses to carry out and allow large-scale firing against Israeli citizens".
Five Israelis sustained light to moderate wounds in Tuesday's barrage, the army said.
The comments, made by a member of Hamas' political bureau, Khalil Al Hayya, came after militants launched what the Israel Defense Forces (IDF) described as the biggest barrage of rocket and mortar fire from the coastal enclave in years.
Prime Minister Benjamin Netanyahu had vowed Tuesday to "respond to these attacks powerfully".
Israel conducts regular air raids on Palestinians in Gaza under the pretext of hitting Hamas targets. But after Hamas wrested power over the strip more than a decade ago, Israel imposed a land and sea blockade on the enclave.
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Later in the day, further rockets or mortar rounds from Gaza were intercepted, the army said.
One mortar shell exploded near a kindergarten building, a military spokesman said, causing damage to the structure. The overnight Hamas rocket fire reached the city of Netivot for the first time since the 2014 war.
The clashes raised fears of another round of conflict in Gaza. Israeli officials signaled they aren't looking for escalation, but warned that continued firing from Gaza could lead to a harsher Israeli response.
Israel stopped short of declaring any formal ceasefire with Hamas and Islamic Jihad, which it, along with Western nations, regards as terrorist organizations, but said any resumption of Palestinian attacks would bring a stronger military response.
In keeping with Israel's policy that every action in Gaza is Hamas' responsibility, the official noted that the terror group was doing nothing to prevent PIJ from sending the projectiles over to Israel.
The high Palestinian death toll in the border protests has drawn strong worldwide criticism of Israel, with rights groups saying Israel's use of live fire is illegal because in many cases it has struck unarmed protesters who did not pose an imminent threat to Israeli soldiers.
But Israel has faced global criticism and calls for an independent investigation over its use of live fire during the protests and clashes along the border.