After four months of intense haggling over an eight paragraph long joint communique, Cyprus's estranged Greek and Turkish leaders will on Tuesday revive stalled peace talks with the aim of once and for all reuniting the island.

Their meeting, at a disused airport in Nicosia's UN-patrolled dead zone, takes place almost two years after the last round of high-level negotiations broke down.

On both sides of Cyprus's ethnic divide, sceptics are already sharpening their pens. There is, they say, an element of deja vu to a psychodrama that has defied resolution by a battalion of mediators for the past four decades. After all, this summer marks the 40th anniversary of the invasion of Cyprus by a Turkish army avenging an attempt to unite the island with Greece. It also marks more than 50 years since a power-sharing arrangement between the two communities collapsed in the wake of independence from Britain.

On both sides, there are two generations who have little or no memory of co-existence.

But this time could be different. A confluence of events – unimaginable a decade ago when the island's two feuding communities came the closest to bridging their differences – has created the conditions for unforeseen hope.

When the Greek Cypriot president, Nicos Anastasiades, meets Dervis Eroglu, the leader of the breakaway state unilaterally declared by the Turkish Cypriots in 1983, he will do so in the knowledge that the stakes are higher than a simple peace on Aphrodite's isle.

In Ankara, Athens and Nicosia, officials are describing the discovery in the eastern Mediterranean of vast oil and natural gas reserves as a game-changer that has made a settlement pressing. Washington, which played an unexpectedly active role in re-igniting the talks, waded in after it became clear that exploitation of the hydrocarbons would require regional stability not only on Cyprus but between Israel and Turkey as well.

The cheapest and most expeditious way of exporting the reserves, discovered first by Israel and then by Cyprus, would be through an underwater pipeline to Turkey. US interest has been dictated partly by the desire to see Europe lessen its dependence on natural gas from Russia.

"We could very well be looking at the beginning of the end of the Cyprus problem," said Hubert Faustmann, associate professor of history and political science at the University of Nicosia. "The big question is how fast or slow they decide to go from here."

Anastasiades admits the "hard work" begins now. The ever-thorny issues of security, territory and property still divide the two communities, as does the idea of either Greek or Turk wielding more power in a "loose federation" of two constituent states that would underpin any form of reconciliation.

But Greek Cypriot officials, who speak of a "seismic shift" in Turkey, have begun to express confidence that hydrocarbons could foster cross-border cooperation – much in the same way that coal and steel helped unite Europe's once warring partners in a community of nations in 1950.

The Turkish foreign minister, Ahmet Davutoglu, called his Greek counterpart, Evangelos Venizelos, at the weekend to convey his "deep pleasure" at the talks being revived.

Analysts say Turkey's beleaguered leader, Recep Tayyip Erdogan, would welcome a foreign policy success in Cyprus, at a time when his scandal-hit government is not only under immense fire but faces unprecedented pressure with municipal elections in March.

Anastasiades, a moderate, calls the chance of peace a "win-win situation". With the internationally recognised southern sector of Cyprus experiencing its worst financial crisis since 1974 and Turkish Cypriots increasingly isolated and impoverished, the time has never been better, he says, for a settlement. "I believe that a solution that would be accepted by the Greek Cypriots would create stability in the region," he said in an interview conducted in his colonial era presidential palace. "Greater co-operation with Turkish Cypriots will contribute to faster growth … to do that you have to have a settlement that is not at the expense of one community or to the benefit of the other."

But while the financial crisis undoubtedly increases the pressure on Greek Cypriots, Anastasiades faces a formidable task of convincing hard-line nationalists. Even if all agree that the West's longest-standing dispute could be resolved in a weekend – given the groundwork covered so far – the result of these latest peace talks will have to be put to national referendums first. The last time a similar referendum was held in 2004, Greek Cypriots overwhelmingly rejected reunification, leaving Turkish Cypriots, who had voted in favour, out in the cold. In his heart Anastasiades knows that when that moment comes, it may well be his most difficult challenge yet.

• This article was amended on 11 February 2014 to correct the Turkish leader's name and a reference to 'natural oil and gas reserves'.