The two men met at the house of Michael Moeller, the U.N. special envoy to Cyprus, Kathimerini reported.
Talat said that Papadopoulos rejected his plan for a preparation time of 2 to 2 1/2 months followed by detailed negotiations, The New Anatolian reported. But Papadopoulos said that Talat turned down his offer of more negotiations next week, Kathimerini said.
Cyprus has been divided for more than 30 years into an area dominated by Cypriots of Greek descent, now an independent country, and a smaller Turkish area.
Moeller called the talks constructive, saying that he expects the two leaders to remain in touch at least through him.
2014: The Year in Music [PHOTOS]