Ahead of Tuesday's final deadline, there were signs that inside the neoclassical palace-turned-hotel hosting the past eight days of talks by armies of technical and legal experts, the end may be in sight.
"Extending the talks is not an option for anyone... We are trying to finish the job," Iran's lead negotiator Abbas Araghchi told Iranian TV late Saturday, saying there was a "positive atmosphere".
But he added: "If we reach an agreement that respects our red lines then there will be a deal. Otherwise we prefer to return home to Tehran empty-handed."
Diplomats said that on one of the thorniest issues -- sanctions relief for Iran -- a compromise may have been worked out, at least among the experts thrashing out the complex final accord.
"There are still differences," an Iranian official insisted, however, while a Western diplomat said that on UN sanctions -- as opposed to EU and US ones -- there was "no agreement yet".
Under the mooted accord, building on a framework deal from April, a complex web of sanctions suffocating the Iranian economy will be progressively lifted if Tehran massively scales down its nuclear programme for at least a decade.
This is aimed at extending the time needed by Iran to produce enough nuclear material for one bomb -- it denies any such aim -- to at least a year from several months at present.
Coupled with more stringent UN inspections, this will give ample time to stop any such "breakout" attempt, while keeping a modest civilian nuclear programme in place in Iran, the powers believe.
Amano saves the day?
The deal between Iran and the P5+1 -- Britain, China, France, Germany, Russia and the United States -- would end a standoff dating back to 2002 when dissidents first revealed undeclared nuclear facilities in Iran.
Thirteen years of rising tensions later, the grand bargain resolving the standoff could potentially put Iran on the road to normalised relations with the outside world -- and at a particularly volatile time in the Middle East.
Such a prospect, however, alarms Iran's regional rival Saudi Arabia and Israel, widely assumed to have nuclear weapons itself and which has lobbied hard to prevent what it sees as too soft a deal.
Iranian Foreign Minister Mohammad Javad Zarif, who has been meeting US Secretary of State John Kerry all week, said in an English YouTube message that a deal could "open new horizons to address important common challenges".
"Our common threat today is the growing menace of violent extremism and outright barbarism," he said in a clear reference to the rampaging Islamic State (IS) jihadist group that is a shared enemy for Tehran and Washington.
On Saturday it appeared that another stumbling block to the deal -- a stalled UN probe into allegations of past efforts by Iran to develop the bomb -- may potentially be close to being resolved too.
Speaking after a whirlwind trip to Tehran, International Atomic Energy Agency chief Yukiya Amano said the UN watchdog aimed to issue a report by year's end on the "clarification of the issues" concerned.
Amano added, however, that this would still require "cooperation" from Iran, which has so far refused to allow the IAEA access to several people and sensitive sites, some of them military, and that "more work" was needed.
"Amano's statement was positive and a significant step toward resolution of the investigation," Arms Control Association expert Kelsey Davenport told AFP.
"If the IAEA is satisfied with parameters of the investigation, then it should be acceptable to the P5+1," she said.