The Israeli prime minister Benjamin Netanyahu has vowed to wipe out Palestinian militants after a night of heavy fire between his forces and the militants.
Mr Netanyahu went straight into military consultations after returning to Israel from the US on Tuesday, where he had been meeting with Donald Trump.
He told pro-Israel lobby the AIPAC that Israel had struck militant sites in Gaza on a scale not seen since the 2014 war with Hamas.
He said: “I can tell you, we are prepared to do a lot more. We will do whatever is necessary to defend our people and to defend our state.”
Israeli troops have been stationed on the Gaza frontier and imposed restrictions on public gatherings after dozens of rockets were fired. One struck a house in the town of Sderot, less than a mile from the border.
The fighting was triggered on Monday morning when a rocket blasted into a house in central Israel, injuring seven people.
The Israeli military said it was a locally made rocket with a range of 75 miles (120km).
Israel’s Iron Dome rocket defence system had not been activated because the attack was unexpected.
Egyptian mediators brokered a ceasefire between the combatants, but firing continued overnight before calm appeared early this morning.
UN mideast envoy Nikolay Mladenov urged the Security Council to condemn the firing of rockets from Gaza, saying it would increase the risk of escalation and a new conflict.
He said 103 rockets and mortars were fired from Gaza towards Israel, with Israel conducting 42 airstrikes in Gaza and firing 16 shells toward Gaza.
Seven Palestinians were wounded and several buildings destroyed.
Commenting on the rockets fired into Israel, Mr Netanyahu said: “Israel will not tolerate this. I will not tolerate this.”
Speaking during a meeting at the White House with US President Donald Trump, he added: “Israel is responding forcefully to this wanton aggression.
“We will do whatever we must do to defend our people and defend our state.”
The renewed violence comes as Mr Netanyahu faces a tough race for re-election on 9 April, with critics accusing him of being too soft on Hamas.