November 20, 2013 06:12 PM (Last updated: November 20, 2013 06:28 PM)
This Sept. 30, 2011 file photo shows Sultan Ahmed Mosque, better known as the Blue Mosque, left, and Hagia Sophia in the historic Sultanahmet district in Istanbul, Turkey. (AP Photo/File)
The feud over the 1,476-year-old World Heritage site is the latest to erupt between the two neighbours over religion.
Greece reacted furiously to remarks by Turkish Deputy Prime Minister Bulent Arinc that he hoped to change the status of Hagia Sophia, which is now a museum.
"We are looking at a sad Hagia Sophia, but hopefully we will see it smiling again soon," Arinc said Monday, describing the complex in Istanbul's historic quarter as the "Hagia Sophia Mosque".
It opened as a museum in 1935 after the founding of modern Turkey.
"Recurrent statements made by high ranking Turkish officials about converting Byzantine Christian churches into mosques are offending the religious feeling of millions of Christians," the Greek foreign ministry said in a statement.
But Turkey bluntly retorted Wednesday that it has "nothing to learn" from Greece about freedom of religion.
"Unfavourable treatment of Ottoman era cultural artifacts and places of worship by Greece is well-known by all," the foreign ministry said in a statement.
Greece whose territory was once part of the Ottoman empire and Turkey share a history marred by bitter territorial disputes and Christian-Muslim feuds.
Mosques have been a thorny issue in Greece, where the population is predominantly Greek Orthodox. Athens is one of the few European capitals without an official mosque.
Arinc, a member of the ruling Islamist-rooted Justice and Development Party (AKP) had said on Monday that two other religious sites in Turkey, also named Hagia Sophia, would be turned into mosques.
The government is often accused by its secular opponents of forcing Islamic values on the predominantly Muslim but strictly secular country.