Israel on Monday issued a brusque warning to Hamas, demanding it prevent rocket fire from Gaza as fears grew of a new confrontation around the coastal Palestinian enclave.

Militants fired 14 rockets at southern Israel during the morning, sending tension soaring and drawing a warning from Prime Minister Benjamin Netanyahu that unless the Islamist movement cracked down on those behind the attacks the Israeli military would step in.

"If this fire continues there are two possibilities: either Hamas stops it as the responsible authority in the area, or we will stop it," Netanyahu said in remarks broadcast on army radio.

"I strongly suggest that Hamas take into account the fact that we will not let this firing continue or expand," he told ministers at the parliamentary committee on foreign affairs and defence.

Since Friday, at least 26 rockets and mortar shells have hit southern Israel, with another four intercepted by the Iron Dome anti-missile system, prompting calls by senior cabinet members for a tough response to Hamas whose powerbase is in Gaza.

In response, the Israeli air force has hit back killing three militants.

The hike in fire from Gaza has coincided with a huge Israeli arrest operation in the West Bank aimed at finding three teenagers who disappeared on June 12.

Israel has blamed militants from Hamas for the attacks.

The Islamist movement had held power in Gaza for the past seven years but stepped down earlier this month when a unified government with the West Bank was sworn in. Despite the change, Hamas remains the de facto authority in charge of security in the Palestinian enclave.

Since June 12, Israel has staged multiple air strikes on Gaza although none were lethal until Friday when two militants were killed, with a third militant killed late on Sunday. The army said all of them were involved in the rocket fire.

Speaking on Sunday, Foreign Minister Avigdor Lieberman reiterated calls for Israel to stage a "full (military) re-occupation" of the coastal enclave from which it pulled out all troops and settlers in 2005.

"At the end of the day, we have seen that limited operations only strengthen Hamas, so the alternative is clear," he said, reiterating his well-publicised stance.

Even Finance Minister Yair Lapid, a relative moderate who heads the centrist Yesh Atid, said it was time to take off the kid gloves and hit Hamas where it hurt.

"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 on Monday.

Despite the calls, Israel's military brass is reluctant to carry out a major ground operation which could cost soldiers' lives and provoke international censure, commentators say.

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 has accused Hamas of kidnapping them, and last week named two of its operatives said to be behind their abduction. Hamas has dismissed the allegations as "stupid".

Israel has said its West Bank campaign is aimed at smashing Hamas's West Bank infrastructure, although there have been growing calls to hit the movement in its Gaza stronghold.

So far, more than 400 Palestinians have been arrested, most of them Hamas members, and five others killed.

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 (PRC) 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.