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The Hagia Sophia opens for Muslim prayer on 24 July.
In a letter to Mr Erdogan, the Council, which counts 350 churches as members, stated the move would sow department.
The president revealed his choice on Friday following a court judgment which annulled its museum status.
The Hagia Sophia was constructed 1,500 years ago as an Orthodox Christian cathedral, but was transformed into a mosque after the Ottoman conquest in1453
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Worshippers prayed outside the building on Friday.