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.
Last week, the Israeli government ordered an intensification of punitive home demolitions in response to the wave of unrest.
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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."
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."
"At this difficult time let us say: Enough is enough," he said.