"I would say we really are beginning that type of negotiation where one could imagine that you could possibly have an agreement," said a senior US official.
However, Michael Adler, an Iran expert from the Woodrow Wilson Centre present in Geneva, cautioned that after last month's ground-breaking visit to New York by Rouhani raised expectations on the nuclear file, "it's clear that there was no concrete progress in Geneva. It's no slam dunk."
Both sides refused to be drawn on the substance of their discussions, and stressed that much more work would be required to strike a deal. But it emerged that Iran laid down a comprehensive plan with a timetable addressing the concerns of both Iran and the West.
According to Iranian Deputy Foreign Minister Abbas Araqchi, Iran is prepared to suspend uranium enrichment at 20 per cent - meeting a prime demand by the West - and agree to give UN weapons inspectors wider scope in Iran to provide greater "transparency".
But, in remarks quoted by an Iranian news agency, he said "neither of these issues are within the first step [of the Iranian proposal] but form part of our last steps."
The bottom line is that Iran is seeking relief from the international sanctions which have hurt its banking and energy sectors, and the right to pursue a peaceful nuclear programme - by continuing to enrich uranium on its own soil.
The West wants guarantees that Iran's nuclear programme is peaceful, and a full accounting of past weaponisation efforts.
The senior US official said there remained differences on what sanctions relief would be appropriate for Iran. "It's clear the 20 per cent enrichment is in play. But if there's no sanctions relief in return, that dynamic is what destroyed the three previous rounds of negotiations," said Adler.
The key to reaching an agreement lies in the sequencing of the concessions to be made by both sides, with negotiators from Iran and the United States looking over their shoulders at hardliners, wary of giving too much away, too soon, in return for too little.
The Obama Administration has to contend with Congress and Israel Prime Minister Benjamin Netanyahu, while Rouhani has the powerful Revolutionary Guards and other conservative foes. However Iranian spiritual leader Ayatollah Ali Khamenei, who has ultimate authority over nuclear strategy, last month expressed support for "heroic flexibility" in diplomacy after Rouhani had a telephone conversation with President Barack Obama at the end of his New York trip.
Zarif stressed that mutual distrust needed to be overcome. Rouhani, who was elected in June, is himself a former nuclear negotiator who forged a deal with the European Union in which Iran froze sensitive nuclear activities in 2003. But the deal broke down amid acrimony with the two sides accusing each other of reneging on their commitments.
Another Iranian former nuclear negotiator, Seyed Hossein Mousavian, said there was now hope for "very serious, real and constructive negotiations". But he too warned that the US Congress remained a major obstacle. "If it doesn't co-operate with Obama negotiations can fail," he told BBC World.
The Geneva talks also involved bilateral meetings between Iranian negotiators and senior officials from the US and UK. Britain and Iran agreed to exchange charges d'affaires within two weeks, according to Iranian media.
