Palestinians have accused Israeli extremists of abducting and killing an Arab teenager and burning his body, sparking hours of clashes in east Jerusalem and drawing charges that the youth was murdered to avenge the killings of three kidnapped Israelis.

Seeking to calm an explosive situation, Israeli prime minister Benjamin Netanyahu urged a swift inquiry into the "reprehensible murder" and called on people to respect the rule of law.

Palestinian president Mahmoud Abbas said it was clear that extremist Jewish settlers were responsible and called on Israel to bring the killers to justice.

"The settlers have killed and burned a little boy. They are well known," Mr Abbas said, accusing Israel of tolerating settler violence toward Palestinians. "I demand that the Israeli government hold the killers accountable."

The death added to already heightened tensions caused by the killings of the three Israeli teenagers, whose bodies were discovered on Monday just over two weeks after they were disappeared in the West Bank.

Israel accused Hamas, the Islamic militant group that controls Gaza, of being behind the abductions, which led to the largest ground operation in the West Bank in nearly a decade, with Israel arresting hundreds of Hamas operatives as part of a broad manhunt.

The discovery of the bodies led to a national outpouring of grief, with tens of thousands of people attending a funeral on Tuesday. As the burial took place, hundreds of young right-wing Israelis marched through Jerusalem screaming for revenge.

Hours later, relatives of Mohammed Abu Khdeir said the 17-year-old was forced into a car in a neighbourhood of east Jerusalem that quickly sped off. A burned body believed to be his was found shortly afterwards in a Jerusalem forest, though police said they were still awaiting forensics tests to make a positive identification.

Police spokesman Micky Rosenfeld said authorities were looking at "a number of different directions" in the killing, including nationalistic or criminal motives. "We are waiting for the final results of the autopsy," he said.

But Abu Khdeir's family said they had no doubt about the killers, accusing extremist Israelis of killing him to avenge the deaths of the Israeli teenagers.

"Who else could do this? There's no one else," said the teenager's father, Saed Abu Khdeir. He said he spent the day with police and gave DNA samples to help identify the body.

Police were also reviewing security camera footage taken from the scene. Relatives said the video showed a car nearing the youth, people stepping out and forcing him into the vehicle and speeding away.

The family of one of the Israeli teenagers condemned the death of the Palestinian youth. "There is no difference between (Arab) blood and (Jewish) blood. Murder is murder," said Yishai Fraenkel, an uncle of one of the three.

As news of the youth's disappearance spread, hundreds of Palestinians in east Jerusalem took to the streets, torching light-rail train stations and hurling stones at Israeli police, who responded with stun grenades and rubber-coated bullets.

The clashes continued throughout the day, emptying streets in east Jerusalem's normally bustling Beit Hanina neighborhood. Masked Palestinians hiding in alleyways and a neighbourhood mosque hurled rocks toward Israeli forces, who occasionally responded with stun grenades.

Two people were taken to hospital with light injuries, police said, and the clashes left a main road littered with stones, debris and burning tyres that spewed black smoke into the air.

The atmosphere in east Jerusalem remained tense well past midnight. Hundreds of Palestinians, many with faces covered, occupied a main road leading into Beit Hanina and the neighbourhood of Shuafat.

Mr Netanyahu urged all sides "not to take the law into their own hands".

But international condemnation came quickly.

In Washington, the Obama administration denounced the killing as a "heinous murder" and called for the perpetrators to be brought to justice.

"There are no words to convey adequately our condolences to the Palestinian people," said secretary of state John Kerry, calling the killing "sickening".

The UN Security Council condemned the "heinous" killing "in the strongest terms" in a press statement, and UN secretary-general Ban Ki-moon called for the perpetrators of the "despicable act" to be promptly brought to justice.

In a statement, the European Union condemned the killing "in the strongest terms" and welcomed Israel's pledge to investigate. It urged all parties to show "maximum restraint".

Despite the calls for calm, fighting continued along Israel's southern border with Gaza.

Militants fired a barrage of eight rockets towards southern Israel, for a total of 20 rockets and mortars fired on Israel throughout the day, the army said. It said anti-rocket defences intercepted two rockets. There were no reports of casualties or damage.

The army said it carried out one air strike on a mortar-launching site in Gaza, scoring a "direct hit".

Early today, a rocket fired from Gaza slammed into a house in the southern Israeli border town of Sderot, causing heavy damage to the structure and a nearby road and knocking out electricity throughout town, the army said. The family was huddled inside a shelter, and no one was hurt, the army said.

In response to the latest rocket barrage, the Israeli military said the air force carried out a "precision strike" on 15 Hamas targets in Gaza overnight, including concealed rocket launchers, weapon-storage facilities and "terror activity" sites.

Palestinian medical officials said 10 people, all civilians, including three women, suffered light to moderate wounds.