Israeli soldiers stand guard in front of Palestinian stone throwers during clashes in the West Bank town of Bethlehem on Monday after Israel's army shot dead a 13-year-old Palestinian.

AFP/Jerusalem

Israel on Tuesday demolished the homes of two Palestinians behind attacks last year after Prime Minister Benjamin Netanyahu pledged an iron fist against mounting unrest.

The demolitions came with Netanyahu under increasing pressure from right-wing members of his coalition, which holds only a one-seat majority, as clashes have spread in recent days following the murder of four Israelis.

The spike in violence has brought international calls for calm, with concerns the unrest could spin out of control and memories of previous Palestinian uprisings still fresh.

The houses destroyed were the former homes of Ghassan Abu Jamal and Mohammed Jaabis, a military statement said. They were placed under demolition orders after the men attacked Israelis last year.

Armed with meat cleavers and a pistol, Abu Jamal and his cousin Uday Abu Jamal killed four rabbis and a policeman before being shot dead in November 2014.

Jaabis rammed an earthmover into a bus in August 2014, killing an Israeli and wounding several others. He was shot dead by police at the scene.

An AFP journalist saw the gutted inside of a house in east Jerusalem that witnesses said was the former residence of Abu Jamal.

Yasser Abdu, 40, a neighbour and friend of the Abu Jamals, accused Israel of a "policy of collective punishment."

The demolition explosion, which took place before dawn, blew out the interior of the structure but the supporting pillars remained intact, an AFP journalist said.

The blast damaged other apartments in the building as well as surrounding structures.

Eyewitnesses said police and other authorities arrived at midnight, locking down the area before drilling and planting the explosives.

A room was also sealed off at the former home of Muataz Hijazi, who in October 2014 tried to gun down a right-wing Jewish activist, critically wounding him. Hijazi was shot dead the next morning during a police raid.

'Intifada' memories fresh  

The demolitions had been challenged in Israel's top court which ultimately approved them months ago.

The court also approved sealing the room but not demolishing the structure, since Hijazi's attack "did not ultimately result in the loss of human life."

The punitive measures come after clashes have spread in east Jerusalem and the occupied West Bank in recent days following the murders of four Israelis, including a Jewish settler couple who were driving with their children in the West Bank.

Israeli security forces said on Monday that five men they had arrested were members of militant group Hamas and had confessed to shooting the couple.

Israeli troops shot dead a Palestinian teenager on Monday - the second killing of a Palestinian in 24 hours - as dozens were wounded in fresh clashes

In the wake of the violence, Netanyahu has announced a series of new security measures and right-wing politicians have urged the demolitions to be brought forward.

"We are not prepared to give immunity to anybody, not to any rioter... or any terrorist, anywhere, and therefore there are no limits on the activities of the security forces," Netanyahu said ahead of a special session of his security cabinet on Monday night.

Also on Monday, thousands turned out in Jerusalem for a rally outside the prime minister's residence organised by Jewish settlers urging Netanyahu to come down hard on militants and boost settlement building.

Israel lifted rare restrictions on Tuesday barring Palestinians from Jerusalem's Old City, with only residents, business owners and students allowed on Sunday and Monday.

The restrictions had been imposed after two Israelis were stabbed to death there and as Jews wrapped up celebrations for their Sukkot holiday, which ended on Monday night.

Worship at the sensitive Al-Aqsa mosque compound will continue to be limited to men aged 50 and above. There is no age limit for women.

Around 300,000 Palestinians live in Israeli-annexed east Jerusalem, where the Old City is located.