NICOSIA - Peace talks between estranged Greek and Turkish Cypriots will resume on May 15, a United Nations envoy said on Monday.Espen Barth Eide was speaking to media after a meeting between Greek Cypriot leader Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci. It was their first encounter since Akinci, a moderate leftist, swept to victory in a Turkish Cypriot leadership election on April 26."They agreed it was important to use the momentum created and opportunity to move forward without delay," Eide told journalists assembled at the Ledra Palace, a landmark hotel straddling a 'buffer zone' in Nicosia, the Cypriot capital, which has been divided for decades on ethnic lines.It is the latest in many attempts to resolve the conflict in the Mediterranean island, split in a 1974 Turkish invasion after a brief Greek-inspired coup. The seeds of division had been sown at least a decade earlier, when power-sharing crumbled into violence just three years after independence from Britain.Eide said the two leaders had agreed to meet on May 15 to have a "general exchange of views" and discuss the modalities and structure of negotiations."This is a unique opportunity, an opportunity to be grasped," said Eide, a former Norwegian foreign minister.Both sides officially agree in principle that the island should be united under a two-state federal umbrella, but past negotiations have foundered on issues such as the competencies of a central government and the residency and property rights of thousands of internally displaced people.The last major peace push collapsed in 2004, when the Greek Cypriots rejected a reunification blueprint accepted by the Turkish Cypriots.