* Biden insists differences in Cyprus not irreconcilable
* Says two sides have agreed to speed up peace talks
* Energy finds spur U.S. interest (Releads, adds detail)
By Michele Kambas
NICOSIA, May 22 U.S. Vice President Joe Biden said on Thursday rival leaders in divided Cyprus had agreed to speed up slow-moving peace talks to heal one of Europe's most intractable rifts.
Biden, the most senior U.S. official to visit the island in more than half a century, said he hoped a solution could be "in reach" to a dispute that for decades has kept Greece and Turkey at loggerheads and their ethnic kin in Cyprus estranged.
Greek and Turkish Cypriots re-launched peace talks in February, in the latest of a long string of efforts to heal the wounds of a conflict that saw a Turkish invasion in 1974 after a brief Greek-inspired coup and the division of the eastern Mediterranean island.
Biden, who hosted a dinner for Cypriot President and Greek Cypriot leader Nicos Anastasiades and Turkish Cypriot leader Dervis Eroglu, said he had seen "common ground" in peace talks, but also differences.
"But I do not believe they are irreconcilable differences. There is clearly a lot of work to be done but what I am hearing gives me hope a solution is within reach this time," he told reporters against the backdrop of a crumbling hotel straddling a United Nations-controlled buffer zone bisecting the capital Nicosia.
Before the Cyprus conflict, the Ledra Palace hotel hosted Hollywood stars. Now the imposing sandstone building, still pockmarked with bullet holes, is used as living quarters for UN peacekeepers.
The Cyprus issue has been given a new dimension by the discovery of natural gas under the sea between Cyprus and Israel, and the significance of the find amplified by the Ukraine crisis and the impact that could have on Russian gas supplies to Europe.
Talking to civil society leaders earlier, Biden said he was convinced Cyprus could "punch well above its weight".
"The possibilities are staggering for this island," he said.
Biden said Eroglu and Anastasiades had agreed to increase the frequency of their meetings to twice a month, and intensify work on preparing "meaningful" confidence-building measures.
"President Obama and I believe that Cyprus is a key partner in a challenging region. And we know it can be an even stronger partner if the next generation of Cypriots can grow up without the burden of conflict," he said.
The breakaway Turkish Cypriot state is recognised only by Ankara. The Greek Cypriot government is internationally recognised as representing the whole island, and represents Cyprus in the European Union, where it has veto rights on the aspirations of Turkey to join the bloc. (Reporting by Michele Kambas; Editing by Andrew Roche)