The statement added that "acts of incitement around the Temple Mount / Haram al-Sharif must be avoided and the status quo has to be respected", using another term for the religious site.
It said, "political, religious and community leaders on all sides should show restraint and responsibility and make every effort to calm down this volatile situation."
More than 200 Palestinians and 17 Israelis police officers were reported wounded when riot police clashed with protesters at the Al-Aqsa mosque compound late Friday, capping a week of violence in the Holy City and the occupied West Bank.
Stones, bottles and fireworks were hurled at officers who fired rubber bullets and stun grenades at the crowds at Islam's third-holiest site, also revered by Jews as the location of two biblical-era temples.
Police said officers had restored order because of the "rioting of thousands of worshippers" after evening prayers.
Tensions in Jerusalem have soared in recent weeks as Palestinians have protested against Israel's restrictions on access to parts of the Old City during the Muslim holy month of Ramadan. Israeli authorities ordered Palestinian families to leave their homes to make way for Israeli settlers, leading to violence and international condemnation.
The EU statement condemned the evictions as "illegal" and blamed them for increasing tensions.
"The situation with regard to the evictions of Palestinian families in Sheikh Jarrah and other areas of East Jerusalem is also of serious concern," it said.
"Such actions are illegal under international humanitarian law and only serve to fuel tensions on the ground."