Mr Guterres is chairing a security conference on Cyprus in Geneva, attended by the foreign ministers of Greece, Turkey and Britain.
Flanked by Greek Cypriot leader Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci, Mr Guterres says he believes Cyprus could be a symbol of hope at a time when the world faced so many disasters.
"You cannot expect miracles of immediate solutions; we are not looking for a quick fix, we are looking for a solid and sustainable solution for the Republic of Cyprus and for the communities of the Republic of Cyprus. And we will be working as time is necessary in order to achieve that goal, with the objective naturally to reach this in the context of the present conference."
Cyprus was split by a Turkish invasion in 1974 that followed a brief coup engineered by the military then ruling Greece.
It has remained split ever since, with Turkish Cypriots in the north and Greek Cypriots in the south.
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Greece, Turkey and Britain are guarantor powers of the island under a convoluted treaty which granted Cyprus independence from Britain in 1960.
Both Greek and Turkish Cypriot leaders face challenges in any power-sharing agreement, ranging from property disputes involving thousands of people uprooted in both sides of the conflict, to ongoing security concerns.
Turkey's foreign Minister, Mevlut Cavusoglu, says the talks are at a critical juncture with discussion likely to continue in the future.
Meanwhile, a spokesman for the Greek Cypriot delegation, Nicos Doulides, called the conference an historic day and hopes the European Union will play a key role in the island's reunification process.
"The European Union is responsible for the security of its member states, is responsible for the European people, so we believe that they have a special role to play and that is why we welcome the presence of Mr Juncker and Mrs Mogherini in Geneva to support us in this difficult discussion. It's a beginning, as very correctly the Secretary General (Guterres) said, it's the beginning of a difficult discussion but we are here - and I can tell you on behalf of the Greek Cypriot community, on behalf of the Republic of Cyprus, we will do our utmost in order to reach a settlement."
An accord has eluded generations of diplomats and NATO allies Greece and Turkey have at times come to the brink of war over Cyprus.
In a groundbreaking move, both sides have submitted proposals on how to define the post-settlement boundaries.
Greek Cypriots make up around 80 per cent of the the population, with the remaining 20 per cent Turkish Cypriots.
Under the proposals put forward, Turkish Cypriots would retain between 28.2 and 29.2 percent of total Cypriot territory, down from about 36 per cent now.
Adding to tensions is the presence of Turkish troops in northern Cyprus, a move strongly criticised by Greek Cypriots.
But Turkish Cypriot leaders say they remain fearful of past experiences when they were targeted by Greek Cypriot nationalists and they want the Turkish military presence to continue.
And within Cyprus attempts are also being made to bridge the divide.
At a community gathering of Cypriots in the island's buffer zone, this woman told Al Jazeera a solution must be found or the divide will become entrenched.
"I feel like it's coming close to a time when we say this is our last chance, because if this situation becomes normalised for generations to come it won't be seen as a problem anymore. To keep our culture of being a Cypriot, we need to fight for unity with people that we share a lot of things with - especially our history."
The United Nations says the next stage of the Cyprus working group will meet on January 18.
