Thursday's talks followed three days of negotiations between Greek Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akıncı aiming to forge a united, two-zone federation.
"We are facing so many situations of disasters. I strongly believe Cyprus can be the symbol of hope at the beginning of 2017", Guterres said.
Speaking to journalists in Geneva after the conference, Turkish Foreign Minister Mevlut Cavusoglu said the Cyprus talks had entered a "critical period" but said gaps still remain on "sensitive issues".
Recep Tayyip Erdogan's remarks came at the end of a week of intense negotiations in Geneva over the reunification of the island, which has been divided since a Turkish invasion in 1974.
But he did not rule out a complete pullout of thousands of soldiers that Turkey keeps on Cyprus as long as Greece, which also deploys a small troop contingent on the island, does the same.
A working group of senior technical experts will meet January 18 in Geneva to hold discussions on critical security issues.
Many residents were stripped of homes and property when Cyprus divided into an official Greek Cypriot south and a breakaway Turkish north where Turkey has more than 35,000 troops stationed.
The arrival of foreign ministers Boris Johnson of Britain, Nikos Kotzias of Greece and Turkey's Cavusoglu brought talks about security a key issue for both Turkish Cypriots and Greek Cypriots to the table for the first time in years of peacemaking efforts. "The results [of the conference] have justified that decision", he said.
The fact that the conference for the first time dealt with the issue of guarantees, seen as the most hard issue facing the negotiators, is regarded as progress in the intractable dispute.
Boris Johnson on his way to meet with Donald Trump's aides
Downing Street has repeatedly dismissed Farage's offer to help her build a relationship with Trump's administration. The Prime Minister and Mr Trump are due to meet in Washington within weeks of his inauguration on January 20.
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.
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.
Turkey has a strong military presence in northern Cyprus.
Ankara opposed the idea of making the European Union a guarantor of Cyprus reunification, considering that the bloc was unable to ensure security on the island and adherence to a reunification deal.
"I really think, without overdramatizing what is happening in Geneva, that it is the very last chance to see the island [reunified]", Juncker told reporters in Malta on Wednesday.
A full withdrawal of Turkish troops from northern Cyprus was "out of the question". Their foreign ministers attended today's discussions. "The negotiation will begin again next week, and when the conditions mature, it will take the form of inter-ministerial [negotiation] with the participation of other representatives", Kotzias said.
The possibility of a reunification pact could hinge on a resolution of security guarantees for a unified Cyprus.
The President added that the proposal that was put forward by the Greek Cypriot side on the security and guarantees issue was the only one discussed at the negotiating table.