Cyprus' rival leaders say they will "significantly intensify" the pace of negotiations aimed at reunifying the ethnically divided island next month because they recognize that "serious work" still remains before any peace deal can be thrashed out.

United Nations envoy Espen Barth Eide says Greek Cypriot President Nicos Anastasiades and breakaway Turkish Cypriot leader Mustafa Akinci had a "constructive exchange" on issues that still separate them over forging a federation.

Speaking after a leaders' meeting late Monday, Eide said both men are aware of the need to keep the momentum going in talks that resumed in May after a monthslong pause triggered by a spat over the island's offshore gas deposits.

Cyprus was split in 1974 when Turkey invaded after a coup aimed at uniting the island with Greece.