Cyprus has been ethnically divided since a Turkish intervention in 1974 triggered by a brief Greek-inspired coup. The dispute, one of the oldest on the UN agenda, has been harming Turkey's decades-old bid to join the European Union.
Peace talks launched between the leaders of the Greek and Turkish Cypriot communities in 2008 have failed to break the impasse.
"Its clear to me and to both leaders that the negotiations have recently come to something of a standstill," said Alexander Downer, the UN special envoy for Cyprus.
"It is clear something has to change."
UN chief Ban Ki-moon scrapped plans for an international conference on Cyprus late this month or early May because insufficient progress had been made in talks, Downer said. He added, however, that Ban still held out hope for a conference in the summer.
The Cyprus conflict has come into sharper focus with natural gas discoveries in the eastern Mediterranean. In moves hotly disputed by the other, Greek Cypriots reported their first major discovery in December, while Turkey launched an on-shore oil drill in Turkish Cyprus on April 26.
Greek and Turkish Cypriots agree in principle on reuniting the Mediterranean island under a federal umbrella, but differ on how that would work.
Crucial differences remain on so-called core issues, ranging from how Cyprus is to be co-governed to settling property claims from thousands of people internally displaced.
Downer said the UN saw no reason to host further meetings of the two leaders "unless there is a clear indication from both sides that there is something substantial they wish to conclude".
"The secretary-general has told the sides it is never too late for bold and decisive moves and new ideas or innovative proposals, but if none are taken then obviously there will be no further convergences on core issues," Downer said.
He said, however, that UN diplomats would have contacts with the two sides over the next two weeks on how the process could move forward. He didn't elaborate, but said it would be about "modalities" of the talks.
"This is not the time to get into some unconstructive and negative blame game. If the talks ultimately founder, there will be plenty of time for that then."