Israel's military, however, said on Saturday that it would hold Hamas responsible for any attack emanating from Gaza.
Among the targets were a training camp of the Hamas group, a military complex used by its naval forces and an underground infrastructure, a military statement said. Dozens of Israelis were treated for injuries as they ran for bomb shelters or stress symptoms.
On Thursday, Israeli military spokesman Jonathan Conricus told reporters that the army had "wanted to keep Hamas out of the fighting".
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The new rocket fire could potentially be attributed to other, smaller militant groups or some factions within Islamic Jihad who are not satisfied by the terms of the cease-fire.
A cease-fire has been in place since Thursday morning following the violent escalation between Israel and Islamic Jihad - the territory's second most powerful Palestinian militant group. By mid-morning, no more projectiles had been fired from Gaza.
On Tuesday, Israel carried out an operation that killed a top commander of Islamic Jihad.
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Islamic Jihad responded by firing rockets into Israel - which then led to retaliatory fire from Israel, killing 34 people in Gaza.
The military said its missile defenses intercepted the two rockets. One strike that flattened a house, killed eight members of a Palestinian family, including five children.
The overnight rocket attack came almost two days after a ceasefire ended a flare-up in cross-border violence between Israel and a smaller Palestinian militant group, Islamic Jihad.
Sirens sounded in the middle of the night in Beersheba, the largest city in southern Israel, some 18 miles from the Gaza border, warning of incoming fire.
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