ISTANBUL — A state-sponsored program to build mosques in countries from Kazakhstan to Cuba has emerged as a foreign policy instrument for Turkey, boosting the country’s claim to a place on the international stage as a leader of the Islamic world that looks after Muslims everywhere.

During a visit to Cuba this week, President Recep Tayyip Erdogan told the government in Havana that Turkey would like to build a mosque in the capital, which would be the first place of worship for the island’s 3,500 Muslims. Erdogan said he was sticking to the project although Cuba’s leaders told him that they had already made an agreement with Saudi Arabia to erect a mosque in Havana.

Turkey’s project for Havana centers on a design inspired by a famous 19th-century mosque in the Istanbul neighborhood Ortakoy on the shores of the Bosporus, Erdogan said. “We told them that ‘we can build the Ortakoy Mosque in another city if you have agreed with others for [a mosque in] Havana,’” Erdogan said. He insisted Turkey wanted to build the mosque alone, without foreign partners.

Erdogan added that the Directorate of Religious Affairs, or Diyanet, a Turkish state institution that administers Turkey’s 80,000 mosques and runs the international mosque-building program via a foundation, and Turkey’s development aid agency, TIKA, would keep track of the mosque project in Cuba. “There has been no negative approach” by the Cuban authorities regarding the Turkish proposal, Erdogan said.