On Saturday officials expressed guarded optimism that after 18 months of tortuous negotiations and two missed deadlines a breakthrough might be in sight for a deal ending 12 years of tensions.
"We're moving forward," Iranian Foreign Minister Mohammad Javad Zarif, hunkered down with US Secretary of State John Kerry in Switzerland since Thursday, told reporters.
"I think we can in fact make the necessary progress to be able to resolve all the issues and start writing them down in a text," Zarif said.
Steinmeier added however that "the final metres are the most difficult but also the decisive ones".
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Russia's chief negotiator, Sergei Ryabkov was quoted by the RIA Novosti news agency as saying the chances of a deal were "more than 50/50".
EU foreign policy chief Federica Mogherini, who arrived late Saturday, said negotiators "have never been so close to a deal" but added there remained "critical points" to resolve.
Russian Foreign Minister Sergei Lavrov and China's Wang Yi were reportedly due to join the talks on Sunday. Britain's Philip Hammond was also expected, completing the line-up.
The mooted deal, due to be finalised by June 30, would see Iran scale down its nuclear programme and allow unprecedented inspections of its remaining activities.