Greece says a UN special envoy has suggested a new name for the Former Yugoslav Republic of Macedonia in a bid to end a dispute over the state's name.
Greece objects to the neighbouring Skopje government using the name Macedonia, saying it implies claims on a Greek province of the same name.
It says UN envoy Matthew Nimitz proposed the name Republic of Makedonia-Skopje for official use.
Greece has said the new name could be a basis for constructive negotiations.
The suggestion uses the name of the capital in the same way that the Republic of Congo-Brazzaville incorporates the name of the city to distinguish it from the neighbouring Democratic Republic of Congo.
Greek Foreign Minister Petros Molyviatis told reporters the suggestion did "not totally satisfy Greece, but it was a basis for negotiations which Greece is ready to partake in a positive and constructive spirit".
But Macedonian Prime Minister Vlado Buckovski reacted coolly to the proposed name.
His government has already offered the solution whereby the international community uses Macedonia and Greece uses Former Yugoslav Republic of Macedonia (FYROM).
"The double formula is on the table. We think that's a greater compromise than the compromise Greece is trying to come up with," he said, according to Reuters.
He said he expected the talks in New York to continue on Monday.
Last year, the United States acknowledged Skopje's use of the name Macedonia, angering the Athens government.
The US said the decision was not meant to anger Greece, but to reward Macedonia for its commitment to democracy.
Greece and Macedonia have held United Nations-led talks on the issue for more a decade. The dispute began with the break-up of the former Yugoslavia in 1991.
Greece imposed an economic embargo on its neighbour until it agreed to be referred to as the "Former Yugoslav Republic of Macedonia" - a name which most of its inhabitants dislike.