More than 70 firefighters were battling the blaze, assisted by five helicopters and two planes, with volunteers also helping.
Turkish President Tayyip Erdogan's move to switch the status of Hagia Sophia to a mosque has struck a raw nerve with many Greeks, who revere the sixth century building as a focal point of their Orthodox Christian faith.
Greece currently uses diagnostic kits imported from a variety of suppliers abroad. The potential new test would use nasal swab samples, two researchers said, and could be available "in the coming future".
Thousands of Greek protesters rallied in central Athens on Thursday against government plans to regulate frequent street demonstrations which often cause disruption in the city.
Greece confirmed 62 new cases of COVID-19 later in the day, bringing the total in the country to 1,735 since its first case wes reported in February. Seventy three people have died.
In a series of statements late on Friday and on Saturday, the Commission approved a 13-billion-euro state aid programme for the Portuguese economy, a 22-billion-euro plan of state guarantees for Poland and a 2-billion-euro scheme for Greece.
The ruling underscores Europe's bitter divisions over migration, though the three ex-communist nations face no immediate penalty as the relocation of tens of thousands of people agreed by the EU was only envisaged until 2017.
MEP Sven Giegold launches new petition
Greece reported its first fatality from the virus on Thursday, in the town of Patra on the mainland. It has confirmed 117 cases of coronavirus so far, including one on the island of Lesbos, where the notorious Moria camp is located.
Tension flared at Greece's mainland border with Turkey early on Friday