Palestinian president Mahmoud Abbas said Tuesday he wanted to avoid a violent escalation with Israel, his most direct comments since unrest has spread in recent days and provoked fears of a new uprising.
His comments came as Prime Minister Benjamin Netanyahu pledged a crackdown and Israel, in a show of force, demolished the homes of two Palestinians who carried out attacks last year.
More clashes also erupted Tuesday, including in Bethlehem following the funeral of a 13-year-old killed by Israeli soldiers during rioting outside the city.
"We don't want a military and security escalation with Israel," Abbas said at a meeting of Palestinian officials, according to official news agency Wafa.
"We are telling our security forces, our political movements, that we do not want an escalation, but that we want to protect ourselves."
Abbas's intentions were unclear before his recent comments, particularly following his UN General Assembly speech last week, in which he declared he was no longer bound by accords with Israel.
But the question remains of whether Palestinian youths frustrated with both Abbas's leadership and Israel's right-wing government will listen to his appeals.
Tuesday's demolitions came with Netanyahu under increasing pressure from right-wing members of his coalition, which holds only a one-seat parliamentary majority, as clashes have spread 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, the military 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 before he was shot dead by police.
An AFP journalist saw the gutted inside of a house in the Israeli-occupied 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.
The demolitions had been challenged in Israel's top court, which ultimately approved them.
The court also approved sealing the room but not demolishing the structure, as 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 West Bank in recent days following the murders of four Israelis, including an Israeli settler couple shot in front of their children.
Israeli security forces said five men they had arrested over the couple's murder were members of militant group Hamas. Netanyahu visited the site of the murders Tuesday.
On Monday, Israeli troops shot dead the 13-year-old Palestinian -- the second killing of a Palestinian in 24 hours -- as dozens were wounded in fresh clashes.
Netanyahu has announced a series of new security measures.
"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 Monday night.
Also on Monday, thousands turned out in Jerusalem for a rally outside the prime minister's residence organised by Israeli settlers urging Netanyahu to come down hard on militants and boost settlement building.
Israel lifted rare restrictions Tuesday barring Palestinians from Jerusalem's Old City, with only residents, business owners and students allowed in the previous two days.
The restrictions had been imposed after two Israelis were stabbed to death there and as Israeli Jews wrapped up celebrations of their Sukkot holiday, which ended 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-occupied east Jerusalem, where the Old City is located.
*This story was edited by Ahram Online.