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"We hope to find a solution to the Cyprus problem by the end of the year, and hold a referendum in the early months of next year so that Cyprus can take on the presidency of the EU as a new state that represents the whole island," Davutoğlu said during a visit to the Turkish Cypriot enclave in the north of the island.
Cyprus was divided by a Turkish invasion in 1974 triggered by a brief Greek-inspired coup. Its Greek Cypriots represent the island internationally and in the European Union, while Turkey is the only country to recognise the Turkish Cypriot state.
The Cyprus dispute is a major obstacle for Turkey's bid to join the European Union, aside from opposition from EU heavyweights France and Germany.
Greek Cypriots say Turkey cannot join the bloc until the Cyprus conflict is resolved.
The EU also expects Turkey to implement the Ankara Protocol, whereby Turkish ports and airports will be opened to traffic from Cyprus. Turkey says the EU should also end its blockade of the Turkish Cypriot enclave.
"A solution will bring real peace to the eastern Mediterranean and truly unite Europe," Davutoğlu said during the joint news conference with the president of northern Cyprus, Derviş Eroğlu.
UN Secretary-General Ban Ki-moon said after meeting Eroğlu and Greek Cypriot leader Demetris Christofias in Geneva on Thursday that he expected the two sides to overcome their differences by October.
Peace talks have stumbled on since being relaunched in 2008. The talks are Cypriot-led, though in coming months the UN team acting as a facilitator could take a more active role.
In principle, both sides agree to reunite Cyprus as a two-zone federation, but they have been unable to reconcile differences ranging from re-drawing existing boundaries to property claims by thousands uprooted in conflict.
Ban said in Geneva that if the sides were able to reach convergence on all core issues - defined by the UN as EU issues, economy, governance, property, security and territory - it would pave the way toward convening a final, international conference.
Territorial and broader security issues involving the roles of Cyprus's guarantor powers - Britain, Greece and Turkey - have barely been touched in negotiations.
Any agreement the two sides reach must go to a plebiscite. In a referendum in 2004 Turkish Cypriots voted for reunification, but Greek Cypriots rejected it.
EurActiv with Reuters