Athens/Nicosia  - Greek and Turkish Cypriot leaders agreed to hold weekly peace talks on Friday in an effort to find a formula and keep the momentum going to reunite the divided Mediterranean island.

It was the fourth meeting between Cyprus President Dimitris Christofias and Turkish Cypriot leader Mehemt Ali Talat since they launched a new round of peace talks on September 3.

Both sides are hoping to end a conflict that has dragged on for decades and which trheatens Turkey's aspirations of joining the European Union. The two leaders are scheduled to meet again on October 13.

"The leaders had further discussions today on the powers of the federal government and they made progress. They also began discussion about the structure of the federal executive," said Special Advisor of the UN Secretary General Alexander Downer in a statement following the three-hour meeting.

"I think it is, from my point of view, very important that the leaders be given plenty of space in order to continue their work."

Peace talks have been deadlocked after former president Tassos Papadopoulos led the Greek-Cypriot rejection of a UN reunification plan in a 2004 referendum.

Turkish Cypriots had overwhelmingly voted in favour.

With newly-elected Christofias in office, expectations are running high for a breakthrough in efforts to reunite the island, which has been divided since 1974 when Turkey invaded the northern third in response to an Athens-led coup to annex the island to Greece.

The two sides have agreed in principle to reunite the island as a federal entity composed of two constituent states, which would guarantee the equality of both communities.

Dimplots fear the peace process, which is barely two months in progress, may already be losing momentum.

"The Greek Cypriot side is not moving rapidly enough as we expect and hoope and they unfairly blame the Turkey side," Burak Ozugergin, spokesperson for the Turkish Cypriot Foreign Ministry told reporters.

The real problem dividing the two sides is how the Greek Cypriot majority would share power with the minority Turkish Cypriots.

The Turkish Cypriots want a loose federation while the Greek Cypriots want a stronger central government and more limited regional powers which will prevent the island falling back into partition.

Meeting at the site of the abandoned, bullet-riddled former airport in the UN buffer zone, both sides have been focusing on the complex list of issues dividing the two sides.

These range from territory and property disputes from more 250,000 people who have lost their homes, to future governance of the island.

Elderly statesmen including former US president Jimmy Carter and Archbishop Desmond Tutu visiting the divided island earlier this week called on both sides to bury their differences at reunification talks, saying failure was not an option.

"Look here man. You could give the world something to smile about, something to celebrate and you have got the capacity to do it," Tutu told journalists at a news conference at a bullet riddled hotel which is now used to house UN peacekeepers in Nicosia. (dpa)