Cypriot leaders have agreed to redouble flagging peace talks to end the island's 40-year division and hold two meetings per month, UN envoy Espen Barth Eide said Wednesday.

The Mediterranean island has been split since 1974, when Turkish troops seized its northern third in response to an Athens-engineered coup in Nicosia aimed at uniting Cyprus with Greece.

Eide said UN-brokered peace talks were accelerating after meeting the island's two leaders -- Greek Cypriot Nicos Anastasiades and Turkish Cypriot leader Dervis Eroglu -- at the UN compound inside Nicosia's buffer zone.

"The leaders agreed to increase also the frequency of their meetings, as appropriate, and to hold meetings at least twice per month," the Norwegian diplomat said.

Eide said negotiators had finished submitting proposals on all issues to conclude the second phase of talks.

He said leaders "had a clear difference of opinion" but would aim in negotiations to tackle unresolved issues stemming from the island's division. These include power sharing arrangements, property rights and territorial adjustments.

Anastasiades said discussions at the meeting were "constructive", and dealt with "the necessity to engage in a substantive dialogue, in order to avert today's situation".

"What I want to see is what will be Mr. Eroglu's conduct at the negotiating table," he added.

The Turkish Cypriot leader Eroglu said he would "try to work in a spirit of 'win-win' towards efforts aiming to pave the way towards a referendum".

"Our main objective is to protect the rights of the Turkish side and to reach a long lasting agreement," he added.

Greek- and Turkish-Cypriot leaders vowed to seek an end to the island's division "as soon as possible" when they relaunched peace talks in February after a nearly two-year hiatus, but progress has been sluggish.

The internationally recognised Republic of Cyprus is still reeling from the eurozone debt crisis, which forced it to secure an international bailout in March 2013 that exacerbated an already severe recession.

Washington is keen to see an end to the division, highlighted by Vice President Joe Biden's landmark visit to Cyprus in May.