Boris Johnson has hailed "real progress" at talks aimed at ending the partition of Cyprus.
Flanked by Nicos Anastasiades and Mustafa Akinci, respective leaders of the island's Greek and Turkish Cypriots, Guterres said the reunification talks had "obviously a way to go".
Instead of seeing four Greek Cypriot presidencies for every one by Turkish Cypriots, Mr Erdogan said he wanted a 2:1 balance in Greece's favour instead.
Foreign ministers of Turkey, Greece and Britain, the three so-called guarantor powers, attended the worldwide conference.
The island was split in a Turkish invasion in 1974 triggered by a brief coup engineered by Greek and Greek Cypriot nationalists trying to unite the island with Greece.
Presented, submitted and then sealed in a United Nations vault, territorial adjustments form an integral part of solving the decades-old Cyprus conflict which has kept Greece and Turkey at loggerheads and obstructs Turkey's membership bid to the European Union.
A working group of senior technical experts will meet January 18 in Geneva to hold discussions on critical security issues.
Turkish President Recep Tayipp Erdogan has clearly said that full removal the country's forces from Cyprus island is "out of question", the sources revealed here on Friday.
The minority Turkish Cypriots see Turkey's military might as their sole insurance against any Greek Cypriot hostility if a peace deal unravels, and insist on keeping the troops as part of a final accord.
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"We are coming very close" to a deal, said Guterres, while warning major work remained on how to implement and guarantee a lasting peace. "The results [of the conference] have justified that decision", he said.
During the talks an it was suggested to dismantle the guarantor system, established by a 1960 treaty, and make the European Union exclusively responsible for the Cyprus unity.
The much-touted United Nations-backed global conference in Geneva aiming to reunify the ethnically split island of Cyprus began Thursday with the participation of leading diplomats from the UN, the European Union and guarantor powers Greece, Turkey and Britain, but no one is expecting a quick fix to a dispute that has defied mediation for 43 years.
Britain, the former colonial power in Cyprus, has offered to relinquish about 50 per cent of territory it still retains on the island, known as sovereign base areas, to facilitate a deal.
The three foreign ministers discussed their guarantor roles established by a 1960 post-independence treaty.
The most sensitive issue is the presence of foreign troops in Cyprus.
Eide told reporters in Geneva that the exchange would take place behind closed doors with cartographers from both sides present.
He added the negotiators were not seeking a "quick fix" but a "solid and sustainable solution". A previous agreement in 2004 was rejected by Greek Cypriot voters.
Given that any deal reached in Geneva would also have to be backed by both communities in separate referendums later this year, Dokos believes that the majority of Greek Cypriots would be more likely to choose the relative safety of the status quo rather than unification, unless the deal stipulated considerable concessions regarding territory, compensation of properties and withdrawal of Turkish troops.