Perched on the tip of Istanbul's historic peninsula, Hagia Sophia -- with its spectacular dome, elegant curves and towering minarets -- is an iconic sight for millions of tourists visiting the city each year.

But should it be a mosque, a church or a museum?

The 1,500-year-old complex overlooking the Bosphorus is at the heart of a bitter dispute over its fate after Turkey's Deputy Prime Minister Bulent Arinc called for it to be converted back into a Muslim place of worship.

His comments, though not official policy, have added to concerns over what critics say is the government's increasing efforts to impose Islamic values on secular Turkish society.

And the Byzantine monument could become a political hot potato for Prime Minister Recep Tayyip Erdogan, who is seeking to shore up flagging support among conservative Muslims ahead of elections next year.

Hagia Sophia, which in Greek means "Holy Wisdom", was built in the sixth century and served as an Orthodox church for centuries -- and as the seat of the Patriarchate of Constantinople -- before being converted to a mosque by the Ottomans in the 1400s.

Greek outcry

Mustafa Kemal Ataturk, the founder of the modern Turkish republic, declared it a museum in 1934 and it opened the following year.

"We are looking at a sad Hagia Sophia, but hopefully we will see it smiling again soon," Arinc said earlier this month.

Greece, whose territory was once part of the Ottoman empire and is often at odds with Turkey over religious issues, reacted furiously, saying such comments offended the religious feelings of millions of Christians.

Mihail Vasiliadis, editor-in-chief of Istanbul-based Greek daily Apoyevmatini, says Hagia Sophia is an important symbol for the entire Orthodox Christian community.

"There are some who have been seeing a sad Hagia Sophia for more than 500 years and they are the ones who want to see it returned as a church," he told AFP.

Istanbul's tiny Greek community, which numbers just a few thousand, is already irked over the issue of Ankara's insistence on reciprocal steps from Athens to improve their religious rights.

"There is no need to add salt to the wound," Vasiliadis said.

Last month, Greece flatly rejected the idea of reviving two mosques in Athens in return for the reopening of an Orthodox clergy school in Turkey.

Two other churches that also bear the name Hagia Sophia have recently been turned into mosques in Turkey.

There are already an estimated 83,000 mosques across the country -- up around seven percent since Erdogan took office 11 years ago.

Istanbul itself has around 3,000, including the stunning 17th century Blue Mosque just a short distance from Hagia Sophia.

For devout Muslims, however, opening Hagia Sophia for worship is also about paying a homage to Fatih Sultan Mehmet, the Ottoman emperor who turned it into a mosque following the conquest of Constantinople and joined the first prayers in 1453.

The nationalist Islamist Great Union Party (BBP) has staged several demonstrations to seek a repeal of the ban on Muslim prayers in Hagia Sophia, part of a UNESCO World Heritage site encompassing the Byzantine and Ottoman treasures of old Istanbul.

Armed with a land registry certificate dated 1936 that describes the complex as a mosque, BBP deputy leader Bayram Karacan claimed that its conversion into a museum was illegal.

"The fact that Hagia Sophia is a museum has never been accepted by the Turkish people... restoring it as a mosque would be akin to reclaiming sovereignty over it," Karacan said.

Outside Hagia Sophia, visitors and local residents were divided over the possible conversion of the monument, described by UNESCO as one of the historic quarter's "unique architectural masterpieces".

"We have plenty of mosques here and many of them are empty. Who will fill all these mosques if it is converted? Tourists will not come here anymore," said 52-year-old shop owner Fehmi Simsek.

Emerging from Hagia Sophia, 23-year-old German tourist Tamara said the complex was a testament to Istanbul's historical and religious importance throughout the centuries.

"Why would you want to change such a remarkable building?"

'Debate linked to elections'

Historian Ahmet Kuyas of Galatasaray University in Istanbul said the debate could be linked to Turkey's upcoming elections, with local polls in March, a presidential ballot in August and parliamentary elections in 2015.

Erdogan, nicknamed the "Sultan", has frequently touched a nerve over his conservative religious policies, including crackdowns on the sale and advertising of alcohol and allowing women working in the public service to wear Islamic headscarves.

"Turning Hagia Sophia into a mosque would be another blow to secular Turkey," Kuyas said, describing the site as "a symbol of universal peace, peace between nations, between religions".

Sevda, a veiled Turkish woman, said it would be more accessible to all as a mosque, as currently there was a fee to enter the museum.

"It belongs to us and therefore it should be a mosque," added her companion Kubra.

A visitor from Spain who gave his name only as Alex said he did not object to a change in the status as long as people could still visit.

"It is a beautiful place that everyone should see," he added.