Ban's visit comes with young Palestinians defying 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.
Israel took further steps today as it sought to deter violence and tamp down what it sees as incitement, destroying the home of a jailed Palestinian attacker in the West Bank and 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 today, 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 wars, checkpoints, harsh responses by the security forces and house demolitions cannot sustain the peace and safety that you need and must have. There is no so-called security solution,” he said.


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