NICOSIA – After Cyprus’ rival leaders failed to agree on returning to Geneva for another Swiss summit aimed at finding a reunification deal for the island that was divided by an unlawful 1974 Turkish invasion, United Nations Special Envoy Espen Barth Eide walked away for now.

“Currently, we have reached a critical juncture in the process, since discussions are underway for the next steps forward,” President Nicos Anastasiades said at a Council of Europe ministerial committee session in Nicosia, repeating diplomatic language indicating there was another stalemate that couldn’t be broken without providing more details.

“I have put forward a creative proposal as to the methodology we could adopt that would allow us to finally break the current impasse, bridge the differences, and establish the parameters,” he said without revealing what it was as both sides continued to cloak the talks in secrecy.

Eide had been shuttling between Anastasiades and Turkish-Cypriot leader Mustafa Akinci but the UN envoy’s usual unstoppable optimism has been burst for now after he couldn’t get them to even lean toward a nod for conciliation.

Eide has said the rival leaders are ready for a final push but that “outstanding issues” had to be cleared up before a summit in Geneva, Agence France Presse said, before he left the island until new talks are scheduled.

Anastasiades said that, “A number of substantial differences still remain which are directly linked to our capacity as an EU member state, and the vital need for a reunited Cyprus to be a truly independent state,” without saying what they were.

Anastasiades is believed to want to resolve what the map of a post-settlement Cyprus would look like and the issue of security arrangements to be tackle, referring to how much property stolen by Turks should be returned and whether Turkey would be allowed to keep an army on the island and invade further if it wants despite the presence of a small UN peacekeeping force.

Eide said some “outstanding issues” need to be cleared up before another summit can be scheduled in a process that’s said to have gone farther than previous reunification attempts over 40 years.

Anastasiades said he has pitched a proposal that could pave the way to a summit. But he decried what he said was a bid to foist responsibility for possible failure on his shoulders.

He criticized the Turkish Cypriot side for insisting on a summit without first committing to resolve how the island’s land would be apportioned as Greek and Turkish Cypriot-administered parts of a federal Cyprus.

Akinci faulted Anastasiades for insisting on tackling outstanding issues individually rather than packaging them together for a final give-and take.

Greek Cypriots want enough territory ceded to their administration that would ensure the return of around 90,000 displaced persons to their homes and properties. However, Turkish Cypriots have offered less.

Akinci said he wants a Geneva conference to address issues of power-sharing and political equality in a federal Cyprus along with allowing a Turk to be President every other term even though up to now Turkish President Recep Tayyip Erdogan won’t recognize Cyprus and bars its ships and planes while he wants to join the European Union – to which Cyprus belongs, apart from the occupied territory.

In a written statement, Akinci rejected what he termed “an effort to put pre-conditions for the Geneva talks” and warned of “new tensions” in the months ahead.

“It is obligatory to discuss in a parallel process all the important issues which have not been solved yet for being able to see the whole picture,” he said, continuing the vague language both sides have used.

“We warn that new tensions could be experienced in the summer months if instead of focusing on the solution, being aware of the fact that time is very tight, the unilateral hydrocarbon explorations continue.”

That was in reference to Turkish demands that Anastasiades bring a halt to planned energy drilling offshore this summer by international companies, including an American firm, and that Turkey have a share in any finds while Erdogan plans to send in a Turkish research vessel to violate Cypriot waters.

(Material from the Associated Press was used in this report)