Rival Greek Cypriot and Turkish Cypriot leaders met Monday in a bid to revive a peace process aimed at reuniting the divided island, but appeared no closer to a breakthrough.

The "clear-the-air" talks between President Nicos Anastasiades and Turkish Cypriot leader Dervis Eroglu were the first between them on the peace process which has been stalled for 19 months.

The meeting, at a restaurant in the UN-controlled buffer zone that has separated the island for nearly four decades, lasted two hours and 40 minutes.

Afterwards, Anastasiades told reporters: "I took this initiative to ascertain whether we could make a joint declaration and open the way to resolving the Cyprus problem."

"Unfortunately there is still a road to travel to reach the desired outcome."

The Greek Cypriot leader said both sides agreed their negotiators should continue efforts to thrash out the terms of a joint statement outlining the objectives of revived peace talks.

There has been no movement in Cyprus reunification talks since March 2012, and the leaders took the unusual step of agreeing to meet informally -- accompanied by senior aides -- without the prompting or presence of the United Nations.

The UN, Russia and the United States welcomed the initiative to hold Monday's talks as a step forward.

Anastasiades said he invited Eroglu to hold the informal talks after the Turkish Cypriot leader called him to pay his respects following the death of Greek Cypriot former president Glafcos Clerides, who was buried last week.

Cyprus has been divided since 1974, when Turkish troops invaded and occupied its northern third after an Athens-engineered coup in Nicosia seeking to unite Cyprus with Greece.