The UN statement came a day after 250 settlers were forcibly removed from the Hebron compound by Israeli security forces acting on an Israeli high court ruling.
The settlers shot and wounded three Palestinians, and hurled rocks at others, as the security operation went ahead.
Violence in Hebron continued on Friday, with dozens of young Palestinians hurling rocks at Israeli troops, who responded by firing tear gas.
In Gaza City, about 2,000 Palestinians took part in a Hamas-led protest against the violence by the settlers.
In the immediate wake of the evictions of Thursday, the south of the occupied West Bank was declared a closed military zone by Israeli security forces.
Right-wing Israelis have vowed to exact revenge for the settlers' eviction.