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 global obligations".
The possible change to the museum's status has been widely condemned internationally.
Transforming it from a mosque was a key reform under the new republic born out of the ashes of the Ottoman Empire.
"As museum, Hagia Sophia can function as place and symbol of encounter, dialogue and peaceful coexistence of peoples and cultures, mutual understanding and solidarity between Christianity and Islam", wrote Ecumenical Patriarch Bartholomew, spiritual leader of Orthodox Christians.
"The decision is meant to score points with Erdogan's pious and nationalist constituents", said Anthony Skinner of the risk assessment firm Verisk Maplecroft.
"Like all our mosques, the doors of Hagia Sophia will be wide open to locals and foreigners, Muslims and non-Muslims", he added.
It warned that the "state of conservation" of the Hagia Sophia would be examined by the World Heritage Committee at its next meeting.
The stunning edifice was first built in the sixth century as a Christian cathedral under the Byzantine Empire as the centrepiece of Constantinople.
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The Council of State issued its ruling in a statement late afternoon July 10, ending a years-long legal process over the status of the Hagia Sophia upon the appeal of an Istanbul-based association.
Earlier in the day, Finance and Treasury Minister Berat Albayrak and Justice Minister Abdülhamit Gül expressed their expectations of opening the Hagia Sophia to worship for the Muslims in separate tweets.
He undermined the Turkish President's plans as anti-Islamic because it says in the Quran that Churches or Synagogues should never be converted into Mosques.
President Recept Tayyip Erdogan signed a decree allowing Moslems to perform prayers in Hagia Sophia, which now enjoys the status of a mosque.
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".
As momentum built for the conversion of the site in recent weeks, many questioned why the status of Hagia Sophia was a priority at a time when Turkey was wrestling with the coronavirus outbreak and the economic outcome of the worldwide pandemic.
It said the decision could lead to even greater divisions. Speaking before the decision was announced, he said, "I am hoping the Council of State reverses this wrong decision, so we can do our prayers in the Hagia Sophia".
On Saturday, police had put up barriers around the Hagia Sophia.