The king, whose country has custodial rights over Muslim and Christian holy sites in Jerusalem, made his remarks in a statement after a meeting with UN chief Ban Ki-moon.
Ban has already met Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas in a bid to get the two sides to rein in violence that has killed 60 people in three weeks.
Angry Palestinians clashed with Israel police over several days in September, spurred by fears Israel is seeking to change the rules governing the site, sparking the latest wave of violence.
The king warned against "any attempt to change the status quo", which Netanyahu has repeatedly promised to preserve.
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The site is the third-holiest in Islam and the holiest to Jews, who call it Temple Mount.
He added that "achievement of a just and comprehensive peace, on the basis of a two-state (Israeli and Palestinian) solution, is the only way out of the crisis in the region."
For his part, according to the statement from the royal palace, Ban stressed what he said was the "responsibility of the international community... To achieve a just and comprehensive solution to the Palestinian question."