UN chief Ban Ki-moon was to make an unannounced visit to Israel and the Palestinian territories Tuesday to try to calm nearly three weeks of violence, even as a new stabbing wounded a soldier.
Young Palestinians have defied an Israeli security crackdown and calls for non-violence from Palestinian president Mahmud Abbas to carry out repeated knife and other attacks on Jews.
There have also been violent protests across the Palestinian territories.
International concern has mounted, with US Secretary of State John Kerry due to meet Israeli Prime Minister Benjamin Netanyahu in Germany this week and Abbas later at an unspecified location in the Middle East.
In the latest incident on Tuesday, an Israeli soldier was stabbed during clashes near the flashpoint West Bank city of Hebron and the alleged 23-year-old Palestinian assailant shot dead.
The stabbing occurred around Beit Awwa in the southern West Bank. Clashes had also erupted in Hebron earlier in the day as Israeli troops destroyed the home of a Palestinian jailed for a deadly knife attack last year.
The demolition occurred as Israel took further steps in its bid to deter violence and tamp down what it sees as incitement, also arresting a senior Hamas official.
Last week, the Israeli government ordered an intensification of punitive home demolitions in response to the wave of unrest.
It says the controversial policy acts as a deterrent but critics say the main victims of such demolitions are relatives forced to pay for another person's actions.
Ahead of his visit on Tuesday, Ban said he understood Israelis' anger at attacks, "when children are afraid to go to school, when anyone on the street is a potential victim."
"But walls, checkpoints, harsh responses by the security forces and house demolitions cannot sustain the peace and safety that you need and must have," he said on UN TV. "There is no so-called security solution."
He also told Palestinians that "I know your hopes for peace have been dashed countless times. You are angry at the continued occupation and the expansion of settlements."
Ban however urged a "peaceful voice for change."
- Heavy security -
The UN chief was expected to meet Netanyahu, who has had an antagonistic relationship with United Nations officials, later on Tuesday and Abbas on Wednesday morning.
At least 42 Palestinians have been killed in the upsurge in violence that began at the start of the month, including alleged attackers. Eight Israelis have died in attacks.
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Israeli security forces have found themselves seeking to clamp down on unrest while not provoking a further escalation of violence.
But checkpoints in Palestinian areas of annexed east Jerusalem, where many of the attackers have come from, and measures such as home demolitions have provoked further anger.
Videos of Israeli security forces shooting dead alleged attackers that have spread online have also fed unrest, with Palestinians seeing some of the shootings as unjustified.
At the same time, the gun, knife and car attacks have sparked fear among Israelis, and some politicians have urged residents to arm themselves in the face of the violence.
Human rights activists blamed such comments in part for an incident on Sunday night, when an Eritrean man was mistaken for an attacker and killed in the southern Israeli city of Beersheba.
The mob violence came after an Arab Israeli gunman also armed with a knife stormed a bus station, shooting dead a 19-year-old soldier and wounding around 10 others.
The gunman was killed, while a security guard at the bus station shot the 29-year-old Eritrean thinking he was a second attacker. A mob also beat him, and the man died later.
Netanyahu warned Israelis against vigilantism after the incident, saying no one should "take the law into their own hands."
- Father of the 'Green Prince' -
Early Tuesday, Israeli troops destroyed the West Bank home of a Palestinian jailed for killing a Jewish settler in a knife attack late last year.
The demolition of the Hebron home of Maher al-Hashlamoun was accompanied by clashes between dozens of Palestinian stone throwers and Israeli soldiers, witnesses said.
Separately, soldiers arrested one of the top West Bank leaders of Islamist group Hamas, Hassan Yusef, in an overnight raid near Ramallah.
The military alleged that Yusef had been "actively instigating and inciting terrorism and publicly encouraging and praising the execution of attacks against Israelis."
Yusef, a founding member of Hamas in the late 1980s, has spent years in Israeli jails. He was elected to the Palestinian parliament from prison in 2006 and was only released from his last stint in jail in June.
He made headlines during the second Palestinian intifada, or uprising, of 2000-2005 when he renounced his son after he admitted to informing for the Israeli security services under the codename Green Prince.