New UN chief Antonio Guterres will attend talks in Geneva Thursday aimed at ending decades of stalemate in a divided Cyprus, in his first foreign trip since becoming secretary-general on January 1.

Foreign ministers from Cyprus's so-called guarantor powers -- Britain, Greece and Turkey -- will also travel to Switzerland for a conference on security, which follows three days of peace talks with the goal of creating a two-zone federation.

Turkish Cypriot leaders have agreed in principle to return some of the land they have controlled since the 1974 invasion by Turkish troops, which came in response to an Athens-inspired coup seeking union with Greece.

UN envoy Espen Barth Eide said Wednesday the sides are very close to agreeing on what overall percentage of the island each will control.

One of the chief difficulties lies in how the boundaries are redrawn, including around the town of Morphou on the northern coast.

Greek Cypriot President Nicos Anastasiades has warned that there can be no deal without a full return of Morphou, while some in the Turkish Cypriot camp have declared its return a non-starter.

The security conference comes after rival Cypriot delegations on Wednesday met to present maps detailing their visions for how internal boundaries should be drawn.

Eide told reporters in Geneva that the exchange would take place behind closed doors with cartographers from both sides present.

"It is a very important moment... Historic," Eide said.

It was to mark the first time since the eastern Mediterranean island was divided that Greek Cypriot and Turkish Cypriot leaders will have presented maps describing the borders of a reunified country, Eide said.

This is the third time the Cypriot leaders have met in Switzerland since November, but the two previous rounds were inconclusive.

- 'The very last chance' -

There were no plans for the maps swapped Wednesday to be disclosed publicly, with the UN hoping that both sides eventually agree on a compromise version.

On Tuesday the two sides also tackled the island's relations with the European Union as well as a future system of government.

While Cyprus has been an EU member since 2004, Anastasiades's internationally recognised government exercises no control over the northern Turkish-ruled part of the island, and EU legislation is suspended there until a settlement is reached.

Eide made clear that the UN process was designed to forge a unified Cyprus that would be a full EU member.

European Commission president Jean-Claude Juncker, who will also be in Geneva on Thursday, said he was making the trip given the stakes of the meet.

"I really think that, without overdramatising what is happening in Geneva, that this is the very last chance to see (a solution for) the island being imposed in a normal way," he said in Valletta at the start of Malta's six-month EU presidency.

Eide has struck an optimistic note during three days of intra-Cypriot talks this week.

"We are roughly where we want to be at this stage," he said Wednesday.

But the sides appear to remain far apart on how many Greek Cypriots should be able to return to homes they fled in 1974, with Akinci determined to minimise the number of Turkish Cypriots who would be displaced for a second time.

There are also still significant differences over security, with Anastasiades wanting Turkish troops to leave the island but Akinci determined to keep a military presence.