Cyprus-Turkey talks go nowhere in Geneva

"As you can imagine, this was not an easy meeting," he added.

"But I do not give up," he said, noting that another mini-summit could take place "in the next two to three months".

"To square the circle is an impossibility in geometry, but it is very common in politics," Guterres said.

He spoke after three days of discussions between the Cypriot president, Nicos Anastasiades, and the head of the self-proclaimed Turkish Republic of Northern Cyprus (TRNC), Ersin Tatar, in Switzerland.

The British, Greek, and Turkish foreign ministers also took part, speaking for the powers which ended UK colonial rule on the island in the 1960 Treaty of Guarantee.

Thursday's talks were meant to help resolve a frozen conflict, which broke out in 1974 when Turkey invaded Cyprus and formed the TRNC.

Previous UN resolutions had spoken of reunification in a "bizonal, bicommunal federation".

But Tatar told Anastasiades he wanted to tear up the old model in favour of full TRNC recognition.

"Nobody should expect us to be patched onto a unitary, single state. We are negotiating for a two-state solution," Tatar said, according to the Reuters news agency.

"Turkish Cypriots and Greek Cypriots have inherent sovereign rights in Cyprus. We are both equal," he added.

"That is why the UN mandate must change ... once we level the playing field, I am confident we will have the breakthrough that we all so desperately want," Tatar said.

And "there is not one single chance of Turkey or the Turkish Cypriot side succeeding in this," Anastasiades told press.

"He [Guterres] made it clear that he could not seek recourse, as was requested by the Turkish Cypriot and Turkish side, to the [United Nations] Security Council for a change to terms of reference," Anastasiades said.

Cyprus has, in the past, vetoed EU-Turkey enlargement talks due to the conflict.

Turkey, a Nato member, has also hampered Nato-EU cooperation due to the old enmity.

More recently, Turkish president Recep Tayyip Erdoğan caused a flare-up in tension by drilling for gas in Cypriot-claimed waters.

He also held a provocative picnic in what was meant to be no man's land in Cyprus, where he voiced backing for Tatar's nationalist vision.

The last UN reunification talks broke down in 2017.

And for his part, Turkish foreign minister Mevlüt Çavuşoğlu also showed there was little chance of a new rapprochement.

Anastasiades had sounded like a "broken record" in his citing of UN resolutions in Geneva, Çavuşoğlu told press.

"We will not make concessions on the issue of [TRNC] independence, sovereignty, and equality," Çavuşoğlu said.

"If these are recognised, the two states can in the future negotiate how they will cooperate. If they are not recognised, we [Turkey and the TRNC] will continue on our path together", he added.