Turkey's military said in a statement earlier on Friday that it had taken power to restore order and democratic rights.
President Tayyip Erdogan and other government officials have described the coup as an attempt by a small faction within the military to seize power, saying it would be defeated.
Greek Prime Minister Alexis Tsipras has discussed the situation in Turkey with Cypriot President Nicos Anastasiades, the official said.
Cyprus was split in a Turkish invasion in 1974 after a brief Greek inspired coup. A Turkish Cypriot enclave in the north of the island is recognised only by Ankara, and the two sides are now engaged in reunification talks.
By late Friday evening, crossings between the north and the south of the island, supervised in part by Turkish Cypriot police under the command of the Turkish military, was unobstructed, a Reuters witness said.
