Israel issued a brusque warning to Hamas on Monday, demanding it prevent rocket fire from Gaza as fears grew of a new confrontation around the coastal Palestinian enclave.
The military said an estimated 14 rockets slammed into Israel early in the morning, although the last struck at around 8.20 am (0520 GMT). Nobody was hurt.
The fire ramped up tensions and brought a warning from Prime Minister Benjamin Netanyahu that unless the Islamist movement cracked down on those behind the attacks the Israeli military would do the job itself.
"If this fire continues there are two possibilities: either Hamas stops it as the responsible authority in the area, or we will stop it," he told the parliamentary committee on foreign affairs and defence in remarks broadcast on army radio.
Since Friday, at least 26 rockets and mortar shells have hit southern Israel, with another four intercepted by the Iron Dome anti-missile system.
The Israeli air force has hit back, killing three militants, but senior cabinet members are demanding a tougher response against the Gaza-based Hamas.
"Israel will not tolerate continued rocket fire at southern Israel and we shall be obliged to take harsh steps if it continues," Foreign Minister Avigdor Lieberman's office quoted him as telling German counterpart Frank-Walter Steinmeier in Berlin.
- 'Harsh blow' -
Even Finance Minister Yair Lapid, a relative moderate who heads the centrist Yesh Atid, said it was time to hit Hamas where it hurts.
"I'm in favour of dealing Hamas a harsh blow, firstly because of the kidnapping... and also because of this firing," he told army radio.
The hike in fire from Gaza coincides with a major Israeli arrest operation in the West Bank aimed at finding three teenagers who disappeared on June 12.
The Israel military told AFP on Monday that to date 420 Palestinians had been detained, including "350 Hamas activists," and 2,200 buildings had been searched.
Israel says Hamas militants snatched the youths.
The military said Monday it has lifted a ban on travel to neighbouring Jordan by residents of the southern West Bank city of Hebron, where the search is focused, "excepted for those connected to Hamas".
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The Islamist movement had held power in Gaza for seven years but stepped down this month when a unified government with the West Bank was sworn in.
But despite the change, Hamas remains the de facto authority in charge of security in the Palestinian enclave.
Since June 12, Israel has staged multiple strikes on Gaza, although none were lethal until Friday when two militants were killed, and a third on Sunday. The army said they were involved in the rocket fire.
The Israeli army says about 40 rockets have struck the south since the three youths disappeared in the southern West Bank on June 12.
Netanyahu last week named two Hamas operatives said to be behind the abduction. Hamas has dismissed the allegations as "stupid".
Israel has said its West Bank campaign is aimed at smashing Hamas's West Bank infrastructure.
- Gaza abandoned? -
Meanwhile, Mussa Abu Marzuk, a top figure in the Hamas politburo, accused Palestinian president Mahmud Abbas of abandoning Gaza in spite of the reconciliation between leaders in the West Bank and Gaza.
"Today, I fear Hamas will be required to come back to protect the security of its people," he wrote on Facebook.
"Gaza does not exist in a vacuum," he said, adding it was not currently ruled by the former Hamas government, nor by the Ramallah-based national unity government which was sworn in on June 2.
Abbas was not taking responsibility for Gaza, and "does not want reconciliation," he charged.
"Even if we give him Gaza, he will not take it."
The confrontations in and around Gaza turned deadly on Friday when two militants from the Popular Resistance Committees were killed by a missile that struck their car in Gaza City.
Another air strike on Sunday evening hit a group of armed men near the southern city of Khan Yunis, killing one of them, sources on both sides said.