At least 14 rockets and mortar rounds fired by militants in Gaza struck southern Israel on Monday morning, causing no injuries but damaging a home, the army said.
The latest incident added to the already-high tension in the area which has seen a surge in rocket fire over the past two weeks.
The rise in rocket fire has coincided with the start on June 12 of a huge Israeli arrest operation in the West Bank aimed at finding three teenagers believed kidnapped by Hamas militants.
Although Israel has staged multiple air strikes on Gaza over that period, none of them were lethal until Friday when Israeli warplanes killed two militants. A third man was killed late on Sunday, with the army saying all of them were involved in firing rockets.
Israeli Prime Minister Benjamin Netanyahu warned Sunday morning he would be ready to expand the military operations.
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Several hours later, two more rockets targeting the southern town of Netivot were intercepted by the Iron Dome anti-missile system in mid-flight, the army said.
Shortly afterwards, another air strike targeted a group of armed men near the southern city of Khan Yunis, killing one of them, sources on both sides said. The military said it had fired on "terrorists in Gaza during their final preparations to launch rockets at southern Israel."
On Saturday night, the Israeli air force had staged 12 raids on sites in Gaza used for "terrorist activity", leaving two people lightly injured after a rocket struck a paint factory in southern Israel, causing an explosion and a big fire.
A day earlier, two militants from the Popular Resistance Committees (PRC) were killed when a missile hit their car in Gaza City. Earlier in the day, a bomb was detonated along the Israeli border, causing no injuries but prompting Israeli tank fire into the Palestinian enclave which medics said wounded five.
The Israeli army says about 40 rockets fired from Gaza have struck the south since the teens disappeared on June 12.
Israel has accused Hamas of kidnapping them, and last week named two operatives of the Islamist movement whom it said were behind their abduction. Hamas has dismissed the accusation as "stupid".
So far, more than 400 Palestinians in the West Bank have been arrested, most of them Hamas members, and another five have been killed.