Cypriot Foreign Minister Nikos Christodoulides, a Greek Cypriot, posted on his official Twitter account that Cyprus "strongly condemns Turkey's actions on Hagia Sophia in its effort to distract domestic opinion and calls on Turkey to respect its worldwide obligations".
The president announced his decision on Friday following a court ruling which annulled its museum status. It was turned into a mosque following the conquest of Istanbul in 1453.
"We urge Turkish authorities to start a dialogue before any decision is taken that could undermine the universal value of the site", it said. The building was finally transformed into a museum in 1935 by Kemal Ataturk, founder of the modern Turkish republic.
But the Council of State, Turkey's top administrative court, said in its ruling on Friday: "It was concluded that the settlement deed allocated it as a mosque and its use outside this character is not possible legally".
Erdogan called upon everyone to respect the government's decision.
Unesco said on Friday its World Heritage Committee would review Hagia Sophia's status and that Turkey's decision raised questions about the impact on its universal value as a site of importance transcending borders and generations.
The Hagia Sophia, a major draw for tourists, has a long and complicated history.
UNESCO said it "deeply regrets" Turkey's decision, especially since the organisation was not informed before the announcement was made.
The court ruled that "there are no provisions whatsoever in the convention (concerning the Protection of the World Cultural and Natural Heritage) that prevents ... the usage of the Hagia Sophia in accordance with domestic law".
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The Council of State had on July 2 debated the case brought by a Turkish group - the Association for the Protection of Historic Monuments and the Environment, which demanded Hagia Sophia be reopened for Muslim prayers.
He told a press conference the first Muslim prayers would be held inside the building on 24 July.
"The decision was taken to hand over the management of the Ayasofya Mosque.to the Religious Affairs Directorate and open it for worship", the decision signed by Erdogan said.
The Ottomans built four minarets, covered Hagia Sophia's Christian icons and luminous gold mosaics, and installed huge black panels embellished with the names of God, the prophet Mohammad and Muslim caliphs in Arabic calligraphy.
The head of the Eastern Orthodox Church has condemned the move, as has Greece - home to many millions of Orthodox followers.
The Turkish president said Hagia Sophia would continue to embrace everyone with its new status as a mosque in a much more honest way.
Orthodox Christian leaders spoke of their deep regret on Friday about the decision.
"We understand the Turkish Government remains committed to maintaining access to the Hagia Sophia for all visitors and look forward to hearing its plans for continued stewardship of the Hagia Sophia to ensure it remains accessible without impediment for all", she added.