Differences between Iran and the west that have so far prevented a historic nuclear deal appear to have narrowed considerably as negotiators gather for a new round of talks in Geneva on Wednesday.
On Tuesday the Iranian foreign minister, Mohammad Javad Zarif, launched a slickly produced YouTube channel with a declaration that the path to a resolution of the decade-old dispute over Iran's nuclear programme was open, and called on the world powers to seize a "historic opportunity".
Zarif's move came as David Cameron spoke on the phone to Hassan Rouhani, becoming the first British prime minister to speak to an Iranian president in a decade.
"The two leaders discussed the bilateral relationship between Britain and Iran welcoming the steps taken since President Rouhani took office, including the appointment of non-resident Charges d'Affaires last week," a spokesperson for the PM said. "They agreed to continue efforts to improve the relationship on a step by step and reciprocal basis."
"On Iran's nuclear programme, both leaders agreed that significant progress had been made in the recent Geneva negotiations and that it was important to seize the opportunity presented by the further round of talks which get underway tomorrow."
The previous round of Geneva talks adjourned early, on 10 November, after an intense and dramatic three days of discussions fell just short of agreement following an intervention by the French foreign minister, Laurent Fabius, to toughen the western bargaining position.
In a Saturday night meeting with the US secretary of state, John Kerry, Fabius insisted that the six powers at the talks – the US, France, the UK, Germany, Russia and France – should not grant Iran's right to uranium enrichment but should demand the cessation of Iran's construction work on a plutonium-producing heavy water reactor at Arak.
Zarif said he would have to consult Tehran on the 11th-hour changes, and the high-level talks broke up.
Since then, there have been clear signs of behind-the-scenes progress. On Sunday, Zarif was quoted in the semi-official Isna news agency as saying Iran's right to enrich was "non-negotiable", but adding that the Iranians "see no necessity for its recognition as a right".
"The right to enrichment does not need to be recognised because, according to the NPT [nuclear non-proliferation treaty], this right is inalienable," the foreign minister said.
If carried through to the negotiating table, the Iranian concession could remove a huge stumbling block. Western officials all accept that some degree of Iranian enrichment is an inevitable part of any eventual settlement but Washington and its allies have been reluctant to put that acceptance in writing as it would create a potentially dangerous precedent. Uranium enrichment is dual-purpose – it can produce fuel both for nuclear power stations and for warheads.
In the western camp, there have also been hints that a compromise could be found over Arak. The French insistence on a complete halt to work on the heavy water reactor was not shared by the whole government, a French defence source said.
"There is a debate going on in Paris, between the Quai d'Orsay [the foreign ministry] and the Élysée [the presidency] on that position," the source said.
German officials are believed to have shared some of the French concerns about a stopgap deal signed in haste in Geneva under pressure to produce results by the presence of Kerry and other foreign ministers. But the Germans disapproved of Fabius's decision to break ranks and make the divisions within the six-nation group public.
Talks since the last Geneva round appear to have resolved some of the differences inside the western camp. "I'm very optimistic there is an understanding. Some of the sensitive work will be shut down. The Europeans are hopeful this will not now be a problem," said Mark Hibbs, a nuclear expert at the Carnegie Endowment for International Peace.
The purpose of the interim deal under discussion in Geneva is to slow down the Iran programme, halting and rolling back some elements, in return for limited sanctions. The deal would last for six months, during which time negotiations would continue aimed at a more enduring settlement.
Among the elements on the table are a halt to Iranian production of medium-enriched uranium, of 20% purity, and a dilution of the existing stockpile of nearly 200kg or its conversion into oxide for reactor fuel. That would add an extra month or so to the time Iran would need to turn it into weapons-grade uranium if it decided to make a weapon.
In return for such concessions, Iran would receive an estimated $10bn (£6bn) in sanctions relief, in the form of unfreezing blocked bank accounts, and the end of restrictions on trade in gold, petrochemicals and aircraft parts.
Officials involved in the talks point out that each of these elements involves separate highly detailed, technical agreements, and so caution that striking a bargain could be a drawn-out and painstaking process.
However, both Washington and Tehran are under pressure to achieve a deal quickly to keep domestic political pressure at bay. The US Congress is threatening to pass new sanctions legislation, which could derail the negotiations.
"The US Congress has recently been seeking to approve a bill to increase sanctions against Iran," said Mohammad-Hassan Asafari a senior member of Iran's parliamentary committee on national security and foreign policy. "It has been decided that the negotiations be suspended if the bill gets through the US Congress."
Iran's president, Hassan Rouhani, warned on Monday in a phone conversation with Russia's president, Vladimir Putin, that "excessive demands" could hamper any possible deal.
"At the recent Geneva talks good progress was made, but everyone must realise excessive demands could complicate the process towards a win-win agreement," the Iranian president told Putin, according to the state English-language television Press TV. "From our point of view, there should not be a situation in which the will of parties to reach mutually acceptable agreement is affected."
The negotiations continue to put a severe strain on US-Israeli relations. Following persistent warnings against striking a deal in Geneva from the Israeli prime minister, Binyamin Netanyahu, Kerry made it clear that he would not be visiting Jerusalem later this week, despite an announcement to that effect made by Netanyahu.
Instead, Kerry's aides said he would try to find time for a trip after the Thanksgiving holiday at the end of November.
On Monday, the secretary of state spoke about Netanyahu's right "to publicly state his position and defend what he believes is his interest". But, in a direct rebuttal of Israel's position, he added: "Nothing that we are doing here, in my judgment, will put Israel at any additional risk. In fact, let me make this clear, we believe it reduces risk."
The progress in Geneva came as the White House also appeared to be holding congressional hawks at bay in Washington.
Barack Obama held a meeting with US senators at the White House on Tuesday to ask them to hold off further sanctions for now while the talks appeared so close to a breakthrough.
Obama revealed details of the proposed deal with Iran during a conference in Washington on Tuesday afternoon.
It would relax some sanctions, but not oil exports or banking, in exchange for a temporary suspension in Iran's nuclear efforts while all sides seek a lasting solution.
"Some of the reporting has been inaccurate, understandably because the [countries involved] have kept the negotiations tight, but the essence of the deal would be that they would halt advances on their nuclear programme, they would roll back some elements that would get them closer to break out capacity where they could run for a weapon before the international community had a chance to react, and they would subject themselves to more vigorous inspections," Obama told a conference of business leaders.
"In return, [we would] open up the spigot a little bit for a very modest amount of relief that is entirely subject to reinstatement if they violate the agreement," he added.
"It would purchase a period of time, lets say six months, during which we could see if they could get to the end state of a position where we, the Israelis and the international community could say with confidence that Iran is not pursuing a nuclear weapon."
Details of the proposed deal, hitherto hazy, may add to pressure from Israel and hawkish Republicans in Washington who say Iran is being let off the hook.