Rival Cypriot leaders Monday turned their sights on the hot-button issues of property and territorial adjustment that for decades have blocked any peace deal on their divided island, the United Nations said.

Territorial adjustments and property compensation remain the most complex and divisive issues in the search for a compromise to end more than four-decade division.

"Today's meeting focused on issues of property and criteria on territory," UN envoy Espen Barth Eide said after the latest round of talks between Turkish Cypriot leader Mustafa Akinci and his Greek Cypriot counterpart Nicos Anastasiades at the UN-controlled buffer zone in Nicosia.

"Regarding property, the leaders agreed that the individual's right to property is respected," Eide said in a statement issued on their behalf.

"Dispossessed owners and current users shall have various choices regarding their claims to affected properties. These different choices shall include compensation, exchange and reinstatement."

Eide said an independent Property Commission will be mandated to resolve property claims based on mutually agreed criteria.

Tens of thousands of people were displaced by the 1974 Turkish invasion, including a population exchange which effectively split the island between a Turkish Cypriot north and a Greek Cypriot south.

Allowing as many Cypriots as possible to return home while adequately compensating those who cannot would boost the prospects of a settlement.

The UN envoy said the leaders were determined to keep up the pace and make progress towards their shared vision of a united, federal Cyprus.

"The leaders also underlined their commitment to maintain the momentum of the process," said Eide.

Many believe the good chemistry between Anastasiades and Akinci can create the climate of trust needed to clinch a long-elusive peace accord.

Key issues that have wrecked previous peace bids are deep-rooted disagreements on territorial adjustments, security, property rights and power sharing in a reunited Cyprus.

- Summer recess until Sept 1 -

Eide also briefed the leaders on the informal consultations he held in New York with the United Nations Security Council last week.

"They welcomed the strong expressions of support of the members of the Council for a settlement in Cyprus," said the Norwegian diplomat.

He said the Security Council was "encouraged" by the work of the two leaders and "recognised the efforts they are making by thinking about the big picture instead of insisting on minor details".

The rival leaders are scheduled to resume talks on September 1 and 14 after a summer recess.

The latest round of UN-brokered peace talks -- widely seen as the best chance in decades to reunify Cyprus -- were launched on May 15.

Any peace accord must be ratified by Greek and Turkish Cypriots at the ballot box.

Cyprus has been divided since 1974, when Turkish troops occupied its northern third in response to an Athens-inspired coup seeking union with Greece.