The head of the United Nations flew into Switzerland earlier today to press Greek and Turkish Cypriots to seal a deal reuniting their east Mediterranean island.
US Vice President Mike Pence has also urged both sides to "seize this historic opportunity".
Diplomatic efforts to reunite Cyprus have failed since the island was divided in a 1974 Turkish army invasion triggered by a coup by Greek Cypriots seeking union with Greece.
However factors such as discovery of gas in the area could increase pressure - domestic and international - for a deal.
UN chief Antonio Guterres flew into the Swiss resort of Crans-Montana, where Greek Cypriot President Nicos Anastasiades and Turkish Cypriot leader Mustafa Akinci have been meeting.
Mr Guterres is due to leave for the G20 summit tomorrow morning, opening only a narrow window for what might be a "final push".
Mr Pence rang both leaders to underscore US support, the White House said in a statement.
"The Vice President urged President Anastasiades and Mr Akinci to seize this historic opportunity to reunify the island and expressed his confidence in both leaders' ability to secure a settlement that would reunify Cyprus as a bizonal, bicommunal federation," the statement said.
Recent major gas discoveries in the Eastern Mediterranean have refocused attempts to end the conflict, partly because the basin could hold sufficient to wean Europe off reliance on Russian gas, but also because of overlapping territorial claims.
Greek Cypriots recently indicated they would go ahead with plans for gas exploration, despite opposition from Turkey.
One diplomatic source said Turkey might be willing to rethink its role on guarantor rights. Turkey, Greece and Britain are guarantor powers of Cyprus in an independence treaty which granted the former colony independence in 1960.
That treaty gives them intervention rights to restore constitutional order.
Turkey has about 30,000 troops in northern Cyprus, a holdover from the 1974 invasion.
Greek Cypriots had previously objected to Turkish Cypriot demands for a rotating presidency, but another source said they had indicated readiness to discuss such an arrangement under conditions.
Any agreement would almost certainly have to go to separate referendums in the Greek and Turkish parts of the island, which each have their deeply-rooted sensitivities born of past communal conflicts.
Negotiators must agree what powers would be held by two probably largely autonomous zones and which would be ceded to any central administration.
It was the second time in a week negotiators had drafted Mr Guterres in to lend his weight to the talks.