The situation of Jerusalem is an exceptional one in that there is no general political agreement as to the status of the city, certain states declaring that they abided by the situation defined in the 1947 United Nations partition plan which considered Jerusalem as a corpus separatum located neither in Israel, nor in Jordan.
The site of Jerusalem was nominated in 1981 by Jordan, it being agreed at the time that inscription should in no way be regarded as a means for registering political or sovereignty claims by any State.
UNESCO's website lists the Old City in the "Arab States" regional group, but does not specify which country it belongs to. UNESCO lists entries for sites in Israel as being part of the "Europe" regional group and they are clearly marked "IL" for Israel.