"Unless all measures go back to what they were before July 14, there will not be any changes," Abbas said in a speech ahead of a meeting with the Palestinian leadership of the date Israel temporarily closed the site after an attack that killed two policemen.
Two days later Israel reopened the site with new security measures, including metal detectors at the entrances, sparking an ongoing boycott of the compound by Palestinians and deadly unrest.
It includes the revered Al-Aqsa mosque and the Dome of the Rock.
The metal detectors were removed by Israel early today, but there are plans to install "security inspection based on advanced technologies and other means", Prime Minister Benjamin Netanyahu's office said.
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Abbas said "all the new Israeli measures on the ground from that date to the present are supposed to disappear".
"Then things will return to normal in Jerusalem and we will continue our work after that in relation to bilateral relations between us and them."