They said that they were prepared to meet again, after holding 90 minutes of talks that focused on the fate of missing persons - one of the thorniest issues that has divided the two communities for decades.
Monday's meeting was the first between the two leaders since the failure of a UN reunification plan for the island that was rejected by Greek Cypriots in a referendum in April 2004 but approved by Turkish Cypriots.
Papadopoulos and Talat shook hands and posed for pictures at the Nicosia headquarters of the UN peacekeeping force in the buffer zone dividing Cyprus.
Both described the meeting as "good" and stressed their support for the work of the UN Committee on Missing Persons (CMP) in Cyprus.
"We exchanged views on the Cyprus problem also," Talat said. "It was a very good and sincere discussion."
Papadopoulos said that both men had expressed "our great support for this humanitarian issue."
"I hope the [missing persons] committee will intensify exhumations and investigations," he said.
Asked by reporters if another meeting was planned, Papadopoulos said: "There is no dogmatic reason for not seeing Talat as long as there is a program of what the meeting will come to."
But he cautioned that any agenda must focus on the core and substantive issues of the Cyprus problem as agreed with UN chief Kofi Annan in February, when it was decided that UN-led technical committees be set up to tackle day-to-day issues to promote trust leading to new talks.
The Committee on Missing Persons "noted with gratitude that the leaders jointly appealed to the international community for urgent and generous contributions" for its work.
Peace talks between the two sides have been on hold ever since the failed 2004 referendum, and Papadopoulos aides made clear that he would limit the agenda of talks with Talat to the issue of people still posted as missing from communal disturbances on the island between 1963 and the Turkish invasion of 1974.
According to the UN the number of missing is 1,468 Greek Cypriots and 502 Turkish Cypriots.
The missing persons committee has warned that because of a shortage of funds, it was launching a small-scale two-month exhumation program beginning in mid-August.
The estimated annual cost of exhumations is $3.3 million, and funding was one of the topics being discussed by the two leaders.
A statement from the committee before Monday's meeting described the August program as "a step in the right direction."
Another opportunity for a face-to-face Papadopoulos-Talat meeting could come during the visit of senior UN envoy Ibrahim Gambari, who is expected on July 6 for a round of contacts with both leaders.
"I'm ready for that," Talat said when asked if he and Papadopoulos would have a joint meeting with Gambari. "Again it depends on what will happen when he visits."
Turkish troops invaded the island's northern third in 1974 following a Greek Cypriot coup in Nicosia by forces seeking union with Greece.
The breakaway Turkish Republic of Northern Cyprus headed by Talat is recognized only by Turkey.
© 2006 Agence France-Presse
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