Israel captured the site in the 1967 Middle East war and annexed it with the rest of East Jerusalem and adjoining parts of the West Bank in a move not recognized internationally.
Jordan, whose ruling Hashemite family has custodianship of the Muslim and Christian sites, appoints members of the Waqf institution which oversees the site.
The Al-Aqsa compound has long been a flashpoint for deadly violence over matters of sovereignty and religion in Jerusalem.
Under the longstanding "status quo" arrangement governing the area, which Israel says it maintains, non-Muslims can visit but only Muslims are allowed to worship in the mosque compound.
Jewish visitors have increasingly prayed more or less openly at the site in defiance of the rules, and Israeli restrictions on Muslim worshippers' access to the site have led to protests and outbreaks of violence.