The meeting of the prime ministers was held on the sidelines of UN General Assembly in New York.
“The prime minister underlined Greece's support of a just and viable solution of the Cypriot problem on the basis of UN resolutions, calling on Turkey to support talks in that process,” according to the statement.
Cyprus has been split in half since 1974, when Turkish troops occupied the northern part of the island, and proclaimed the Turkish Republic of Northern Cyprus, recognized only by Turkey, in 1983.
According to the statement, Tsipras and Davutoglu also discussed cooperation in tackling the ongoing refugee crisis as well as collaboration in the spheres of trade, culture and transport.
Greece is one of a number of EU member states most affected by a massive inflow of refugees, fleeing conflict-torn countries in the Middle East and North Africa. According to the UN refugee agency, about 390,000 refugees have crossed the Mediterranean Sea to Greece this year, mostly via Turkey.