Palestinians carry the body of 16-year-old Mohammed Abu Khdeir in Jerusalem. (AP Photo/Mahmoud Illean)

Jerusalem - Israeli police have arrested a group of Jewish extremists in connection with the kidnap and murder of a Palestinian teenager who was burned to death in a suspected revenge killing.

The brutal killing on July 2 has triggered four days of violent clashes which began in east Jerusalem and have since spread to more than half a dozen Arab towns in Israel, with hordes of angry protesters hurling stones at Israeli riot police.

“Apparently the people arrested in relation to the case belong to an extremist Jewish group,” an official said, speaking on condition of anonymity.

The website of Haaretz newspaper said six people had been arrested, but details of the case have been subjected to a strict gag order.

Earlier, police acknowledged for the first time “indications that the background to the killing was nationalistic”.

It followed days of growing suspicion that Wednesday's murder was carried out by extremist Jews in revenge for last month's abduction and murder of three Israeli teenagers in the occupied West Bank.

Tensions continued to rise in the south Sunday with Gaza militants firing another 15 rockets over the border, despite a night of 10 air strikes. The air force also staged another strike in the afternoon, which caused no casualties, Gazan officials said.

But Israel appeared bent on containing the situation, with Prime Minister Benjamin Netanyahu urging his cabinet to keep a cool head over how to handle growing tensions in and around Gaza.

Overnight, Israel police arrested 35 people as violent protests over the teenager's murder swept more than half a dozen Arab Israeli towns.

The violence exploded as a top Palestinian legal official confirmed that initial findings from the post mortem showed there was smoke in the lungs of 16-year-old Mohammed Abu Khder, indicating he was still alive when he was set on fire.

The grisly murder has sparked shock, disgust and an outpouring of condemnation from both Israeli and Palestinian leaders.

But until Sunday, police said they were unsure of the motive for the killing, contributing to the rising tensions.

“Around 35 people were arrested overnight, almost half of them minors,” police spokeswoman Luba Samri told AFP after violence raged into the early hours of Sunday.

Of those, 22 were detained in and around the northern city of Nazareth, Israel's most populous Arab town.

The rest were arrested in the so-called Triangle, a concentration of Arab towns and villages close to the northwestern sector of the Green Line ÄTaibe, Tira, Qalansuwa, Jaljulia and Umm el-Fahm.

“We are demonstrating against this incitement to hatred by Israelis online, who are saying 'death to Arabs',” one demonstrator in Qalansuwa told army radio.

In a related development, a Jerusalem court freed a Palestinian American teenager, who was allegedly beaten in police custody, to house arrest for nine days pending an investigation into stone-throwing allegations.

Tariq Abu Khder, 15, a cousin of the murdered teen, was arrested on Thursday in the east Jerusalem neighbourhood of Shuafat as clashes raged, and his parents said he was badly beaten in police custody.

A day after his arrest, a video surfaced on YouTube showing Israeli border police beating and kicking a handcuffed semi-conscious figure on the ground, before dragging him away.

Washington said it was “profoundly troubled” by the report, prompting the Israeli justice ministry's police investigations department to begin an urgent investigation.

Meanwhile, Netanyahu demanded that his cabinet keep a cool head about growing tensions in Gaza.

Over the past three weeks, militants there have stepped up rocket fire on southern Israel, causing damage but no injuries, prompting demands for a new military operation in the coastal enclave.

So far, Israel has responded with air strikes, killing three militants, but Netanyahu has resisted calls for tougher action.

“Experience has proved that at moments like this, we have to act responsibly and with a cool head and not with harsh words and impetuousness,” he told the weekly cabinet meeting.

Ministers are fiercely divided over how to respond to mounting militant rocket fire, with far right Economy Minister Naftali Bennett and Foreign Minister Avigdor Lieberman pushing for a broad operation against Gaza.

Overnight, the air force staged 10 strikes on Gaza after militants fired 15 rockets and mortar rounds at Israel, two of which targeted the southern city of Beersheva some 40 kilometres (25 miles) away.

There was another air strike on Sunday afternoon.

Meanwhile, the army arrested a Palestinian in the flashpoint southern West Bank city of Hebron, with unconfirmed reports saying he was connected to the murder of the three Israeli teens.