Anastasiades and Akinci met earlier this month, between November 7-11, to discuss potential territorial readjustments.
The latest round of talks between rival leaders on ending Cyprus's 42-year-old division broke up without agreement on Tuesday, the United Nations said.
Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Mustafa Akinci have been meeting on the shores of Lake Geneva since Sunday in the second round of talks this month.
"Despite their best efforts, they have not been able to achieve the necessary further convergences on criteria for territorial adjustment that would have paved the way for the last phase of the talks," UN spokesman Aleem Siddique said in a statement.
"The two sides have decided to return to Cyprus and reflect on the way forward."
The talks are aimed at reunifying Cyprus, a Mediterranean island whose division remains one of the world's longest-running political disputes.
The island has been divided since 1974 when Turkish troops occupied its northern third in response to an Athens-inspired coup seeking union with Greece.
Anastasiades and Akinci met earlier this month, between November 7-11, to discuss potential territorial readjustments -- seen as the trickiest issue to resolve.
That round finished short of a deal but hopes had been high that the second round could produce a map of internal boundaries for a future federation of Greek- and Turkish-speaking states on the island.
The Turkish invasion saw thousands of Greek and Turkish Cypriots displaced.
Territory is an intractable problem for the talks, since any agreement would inevitably involve a redrawing of existing boundaries and see members of both communities ousted from their current homes.
The leaders had been thought to be close on the percentage of territory to be governed under Turkish Cypriot jurisdiction, with Akinci suggesting 29.2 percent and the Greek Cypriots proposing 28 percent.
The sticking point is which towns and villages come within those boundaries.
The UN and outgoing Secretary General Ban Ki-moon have staked much on solving the conundrum.