President Tayyip Erdogan has proposed restoring the mosque status of the UNESCO World Heritage Site, a building at the heart of both the Christian Byzantine and Muslim Ottoman empires and today one of Turkey's most visited monuments.
The court case disputes the legality of a decision in 1934, in the early days of the modern secular Turkish state under Mustafa Kemal Ataturk, to convert the huge sixth-century building – known in Turkish as Ayasofya – from a mosque into a museum.
"We think they (the court) will see that Ayasofya being a museum for 86 years has hurt and saddened the Turkish people," Selami Karaman, lawyer for the association which brought the case, told reporters after the short hearing.
"This mosque... is the personal property of Sultan Mehmet the Conqueror," he said, referring to the Ottoman leader who captured the city, then known as Constantinople, in 1453 and turned the already 900-year-old Byzantine church into a mosque.
The Ottomans built minarets alongside the vast domed structure, while inside they added huge calligraphic panels bearing the Arabic names of the early Muslim caliphs alongside the monument's ancient Christian iconography.
Ecumenical Patriarch Bartholomew, the spiritual head of some 300 million Orthodox Christians worldwide and based in Istanbul, said converting it into a mosque would disappoint Christians and would "fracture" East and West.
US Secretary of State Mike Pompeo and Greece have also urged Turkey to maintain the building as a museum.
But Turkish groups have long campaigned for Hagia Sophia's conversion into a mosque, saying this would better reflect Turkey's status as an overwhelmingly Muslim country.Erdogan, a pious Muslim, threw his weight behind their campaign ahead of local elections last year.