Erdogan acknowledged after holding talks with Cuban President Raul Castro in Havana that Cuban officials had appeared to have already made an agreement with Saudi Arabia for the construction of a mosque in Havana.
But Erdogan, who caused astonishment last year by claiming Muslims discovered the Americas before Columbus, said Turkey was pressing for an Ottoman-style mosque in another city in Cuba.
"We have told them that we could build a similar one to Ortakoy Mosque in another city, if you have promised to others for Havana," Erdogan said in the communist island, the second stop of his Latin America tour.
The neo-Baroque edifice is a familiar sight on the shore near the Bosphorus Bridge.
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Erdogan said Turkey was not in search of a partner to build the mosque as "our architecture is different from that of Saudi Arabia."
"I have provided the Cuban officials with all the necessary information.... So far they have not taken a negative approach to it," he was quoted as saying by the presidential website.
Erdogan, a pious Muslim who has been in power for more than a decade, stirred controversy late last year by declaring that the Americas were discovered by Muslims in the 12th century, nearly three centuries before Christopher Columbus sailed across the Atlantic.
The president has repeatedly been ridiculed by critics for harking back to Turkey's past to even before the Ottoman Empire was established in the fourteenth century.