Israel is "ready" to expand its operations in Gaza, Prime Minister Benjamin Netanyahu warned Sunday after the air force struck 12 targets overnight following a surge in militant rocket fire.

Speaking to ministers at the weekly cabinet meeting, the Israeli premier said the almost-nightly military strikes on Gaza could be expanded should the need arise.

His remarks came after a sharp hike in tensions along the border as militant groups have stepped up their fire on southern Israel.

"Over the weekend, the IDF attacked multiple targets in response to firing at Israel from the Gaza Strip. We are ready to expand this operation as per need," Netanyahu said, without elaborating.

Speaking to army radio ahead of the cabinet meeting, Israel's hawkish Foreign Minister Avigdor Lieberman warned a limited response would only strengthen the Islamist movement Hamas, which 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.

"We have seen that, at the end of the day, limited operations only strengthen Hamas so the alternative is clear," he said, repeating his long-held assertion that Israel should re-occupy the Gaza Strip, which it left in 2005.

Israeli warplanes struck Gaza 12 times overnight, with Palestinian officials saying two people had been lightly injured.

The army said the sites targeted were being used for "terrorist activity."

The raids took place after six rockets struck southern Israel on Saturday evening, one of which hit a paint factory in Sderot industrial zone, causing an explosion and major fire as the flammable substance ignited, police said.

On Friday, two Palestinians were killed in an Israeli air strike on a car near Gaza City, with the military saying they had been involved in firing rockets at Israel.

Hours earlier, a bomb had exploded along the southern sector of the border, prompting Israeli tanks to open fire towards the southern city of Khan Yunis, injuring five Palestinians, one of them a child.

The military said it had fired on "lookout posts used to guide the attack" with Palestinians officials saying it had targeted "two mosque minarets east of Khan Yunis."

Over the past fortnight, 25 rockets fired from Gaza have struck southern Israel out of a total of 28 since the start of the month, prompting a series of almost nightly Israeli air strikes. Last month, the total was seven.

The rise in rocket fire has coincided with a huge Israeli arrest operation in the West Bank to track down three teenagers who went missing on June 12, whom Israel says were kidnapped by Hamas militants.

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

But there has been no claim for the youths' abduction, nor has there been any indication of their whereabouts.