Guterres had met President Nicos Anastasiades and President of the Turkish Republic of Northern Cyprus Mustafa Akinci in the German capital for "informal, trilateral" talks of reviving long-stalled peace negotiations.
The Turkish government is standing firm on its oil and gas exploration in the Eastern Mediterranean as Greece and Greek-administered Cyprus call on the European Union to take action against Turkey.
Greek Cyprus President Nicos Anastasiades' decision comes after justice minister resigned amid criticism of police for mistakes in following up on the disappearances of some of the women and girls that an army captain claims to have killed.
Both sides exchanged views on the issue of extending the jurisdiction of founding states, in a possible solution to the Cyprus issue.
The opening of the Dherynia border post in the east and the Lefka crossing in the northwest is the first such step to end the 44-year frozen conflict between Turkish Cypriots and Greek Cypriots in eight years.
UN secretary-general’s personal envoy Jane Holl Lute held separate meetings with Turkish Cypriot President Mustafa Akinci and Greek Cypriot leader Nicos Anastasiades to test possible restart of reunification talks.
Turkey's criticism comes after Ankara deployed navy vessels on Friday to stop a rig belonging to the Italian energy firm ENI as it headed toward an area southeast of Cyprus.
Nicos Anastasiades won re-election as Greek Cypriot leader since voters gave a thumbs-up to his record in containing an economic meltdown in 2013 and conducting abortive peace talks with the Turkish Cypriots.
The two leading candidates to emerge from Sunday's election will have to seek support from the seven other candidates ahead of the February 4 ballot.
Turkish and Greek Cypriots remain in limbo as both sides brainstorm ways to proceed with suspended peace talks, with the fate of their island resting on the shoulders of one undecided man.
UN Secretary General Antonio Guterres said there was still a wide gap between all the parties involved on a number of issues and called for fresh initiatives to address the ethnic division of the island.
Turkish troops have been in northern Cyprus since 1974. The international community deems this to be an "occupation" of a sovereign state, but Turkey insists the measure is both legal and necessary.
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