"We were not able to stitch it together to a final deal. That was a blow I think to everybody involved, and the question is what we can do now," Eide told reporters in Nicosia.
He said the process was now in "a cooling off phase".
The Norwegian diplomat returned to the island for his first talks with the rival Greek and Turkish Cypriot leaders of the divided eastern Mediterranean island since UN-mediated negotiations collapsed on July 7 in the Swiss resort of Crans-Montana.
The Norwegian diplomat said the United Nations has not closed the door on reviving a process than many observers feel has reached a dead end.
"I am not giving up, the UN is not giving up, but at the same time I do not want to create any false illusions, I want to be honest," he said.
"I do not see any immediate developments, I haven't heard anything here that suggests something will happen in the very near future, there is a cooling off phase going on now," he said after their meeting.
The negotiations between Anastasiades and Akinci broke down after the United Nations failed to broker a compromise deal on a new security arrangement for a post-solution Cyprus.
Greece wanted to end the right of intervention on Cyprus it holds with Britain and Turkey, while Nicosia was also pushing for a withdrawal of Turkish troops stationed on the Mediterranean island and EU member state.
"Turkey has been clear all the time that they can not except both zero guarantees and zero troops," said Eide.
He said at Crans-Montana that the UN was working towards ending guarantees and intervention rights but some foreign troops would have stayed on the ground.
Both Nicosia and Athens have accused Eide of having been "unprepared" in Crans-Montana and then of not giving a full picture of what happened in the Alpine ski resort.
Turkey maintains around 35,000 troops in the north, while Akinci heads a self-declared statelet recognised only by Ankara.
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