Palestinians set fire to a shrine in the occupied West Bank and an attacker disguised as a journalist stabbed an Israeli soldier as tensions ran high after more than two weeks of violence.
Israel's military said about 100 people converged on the tomb of the biblical patriarch Joseph in the Palestinian city of Nablus and set parts of it ablaze before Palestinian security forces arrived and pushed them back.
Hours later, a Palestinian posing as a journalist wounded anIsraeli soldier with a knife before being shot dead near thetown of Hebron, the Israeli military added.
Reuters television footage showed the Palestinian rolling on the ground and surrounded by Israeli troops after the attack.
He was holding a knife and wearing a fluorescent yellow vest over at-shirt marked "PRESS".
A military statement about the shrine attack said: "We view this incident with gravity and strongly condemn any attack on holy sites. We will find and arrest those who set the fire."
Joseph's tomb has been venerated for centuries by Jews, Samaritans, Christians and Muslims.
Palestinian President Mahmoud Abbas condemned the attack and ordered the damage to be repaired.
He also opened an investigation into the attack.
A statement from his office said Mr Abbas "stressed his rejection of these actions and all actions that violate law and order, and which distort our culture, our morals and our religion".
Violence also broke out in the Gaza Strip when Palestinians approached the border fence with Israel.
The soldiers reportedly opened fire after Palestinians began throwing stones, killing a Palestinian and wounding 27others, Palestinian medical officials said.
The Israeli military said hundreds of people gathered along the border, some hurling rocks and burning tyres at the fence.
A military spokeswoman said troops "are operating to prevent further escalation of violence using riot dispersal means andfiring towards main instigators."
The unrest has erupted mostly in Jerusalem and the occupied West Bank and is the most serious in years, claiming the lives of 35 Palestinians and seven Israelis.
The Palestinian dead include children and protesters shot during demonstrations, as well as 11 people described by police as knife-wielding assailants.
One man died in Gaza on Friday from wounds sustained in a clash a week ago.
The Israelis were killed in random attacks in the street or on buses.
The UN Security Council is to hold a special meeting to discuss the situation.
No resolution is planned for today, but there might be an attempt to get the council to issue a statement urging the two sides to curb the violence.
Hamas, which controls the Gaza Strip, called for "rallies of anger and confrontations" in all West Bank cities.
"Our decision is to pursue the Intifada (uprising) andc ontinue the resistance against the Israeli occupation," said Ismail Haniyeh, the group's leader in Gaza.
The unrest has been triggered in part by Palestinians' anger over what they see as increased Jewish encroachment on Jerusalem's al-Aqsa mosque compound, which is also revered by Jews as the location of two destroyed biblical Jewish temples.
The director-general of Israel's foreign ministry, Dore Gold, said: "The burning of Joseph's tomb forcefully demonstrates what would happen in the holy places in Jerusalem if they were in the hands of the Palestinian leadership."
US Secretary of State John Kerry has said he plans totravel to the Middle East soon to try to calm the violence.
Israeli Prime Minister Benjamin Netanyahu said he was ready to meet Abbas to help restore calm.