Three Israelis accused of kidnapping and burning to death a Palestinian teenager have reportedly confessed and re-enacted the murder for the authorities.

The three are among six people arrested for the killing last week of Mohammed Abu Khdeir, which investigators believe was revenge for the death of three Israeli teenagers. The mother of one of those accused, however, denied his involvement, telling the Ynet website: "We're shattered and this thing is very difficult for us. My son has nothing to do with this and he will go free. This is crazy because he's only 16."

News of the reported confessions came as police struggled to contain violent clashes in occupied East Jerusalem and in Arab towns across Israel that have plunged many areas into a toxic and fearful divide.

Tensions have been running high for weeks since the Israeli teenagers were kidnapped and killed in the West Bank.

Last week, hours after the Israeli teenagers were buried, 16-year-old Abu Khdeir was abducted from outside his home in East Jerusalem. His charred remains were found later in a Jerusalem forest.

The crisis comes against a background of increased tension on the Gaza border, which has seen weeks of increasing rocket fire into Israel and Israeli airforce airstrikes. Dozens of rockets were fired from Gaza into Israel on Monday, including 40 launched in a single hour after nightfall, setting off air raid sirens up to 50 miles (80km) from Gaza, the Israeli army said. Twelve rockets were intercepted by rocket-defence batteries, it added, and the others landed in open areas. It was the deepest penetration of rocket strikes in the current round of fighting and raised the likelihood of an even tougher Israeli response.

An Israeli strike on Sunday killed nine Palestinians, including seven members of Hamas, which vowed retaliation.

According to an Israel Defence Forces spokesman, the seven Hamas members were killed when they returned to a tunnel that had been attacked three days ago and accidentally detonated explosives.

He added that two brigades on the Gaza border and 1,500 extra reserve troops had been put on notice of "preparedness for escalation", but they had not been ordered to mobilise for an operation into Gaza.

Amid the tensions, there has been growing anxiety among ordinary Israelis and Palestinians. Roads entering Palestinian neighbourhoods in East Jerusalem from the west and centre are eerily quiet after days in which many have been closed. Police stand on footbridges and over passes. There are few Palestinians visible in the city centre. On social media and in meetings at schools, fearful parents of Jewish and Palestinian communities have discussed how to protect their children.

On Saturday evening in Jerusalem's central Zion Square, after a small peace rally, small groups of participants wandered off into the night to walk and keep watch in Palestinian neighbourhoods against incursions by rightwing Israeli groups.

Across Palestinian neighbourhoods of the city, from Beit Hanina to the deep cut valley of Silwan, residents have formed neighbourhood watch groups, patrolling their streets and checking strangers' cars.

At a community centre and youth group in Silwan Jawad Siyam, the centre's director said few people from his neighbourhood were going west of the green line. "I'm not really going. I went today to have a look around but I didn't get out of the car. I didn't see any Palestinians but I saw [Jewish] radicals walking around.

"Usually we leave the door of the centre open here all the time so people can access the kitchen but the first night settlers tried to come in and the police did nothing. Now 10 of us stay up during the night and stay in the street till daylight.

"Because we have a park some parents come here from other neighbourhoods, but not since the murder [of Abu Khdeir]."

The fear is not only in Jerusalem but in wider Israel. Israeli Arabs have been assaulted in public places, while Jewish cars in Arab towns have been attacked and individuals stoned.

But the fear is being driven most by rumours, almost daily stories on both sides and fuelled by social media, of new "kidnappings" or attempts.

By Monday , disturbances had been reported from Israel's south, where Bedouin protesters clashed with Israeli security forces in the Negev, to Arab towns in the north and across the green line in the occupied West Bank. Walking with her two young children, aged six and seven in Independence Park, a woman who would only give her name as Irit said: "Of course I am nervous. Everyone is anxious. Because they can't see at the moment where this is going to end." Israel's outgoing president, Shimon Peres, and his successor, Reuven Rivlin, promised in a joint editorial published in Yedioth Ahronoth, the country's best-selling newspaper, on Monday that there would be no cover-up in the investigation of Abu Khdeir's death.