Adding to the drama, Russian Foreign Minister Sergei Lavrov left the crunch talks with Iran in Switzerland after a series of meetings, Russian media reported.
He will only return if there is a "realistic" chance of a deal, his spokeswoman said earlier.
Lavrov and his counterparts from the United States, China, Britain, France and Germany met with the Iranians in a lakeside Lausanne hotel today for their first full session since missing a previous November deadline.
Global powers have set a midnight Tuesday deadline to agree the outlines of a deal that they will then try to finalise by June 30. Only then would Iran receive sanctions relief, diplomats said.
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The global powers want Iran to scale back its nuclear programme to give the world ample notice of any dash to make the bomb and end a crisis that has threatened to escalate dangerously for 12 years.
The threat of new US sanctions, and domestic pressure on Iranian President Hassan Rouhani for his attempts at rapprochement with the West, all but rule out any further extension of the deadline.
"We had a very important meeting, and detailed discussions," Iran's lead negotiator Abbas Araghchi said, while insisting "we have solutions" for most of the remaining issues.
Even before a deal is sewn up, opponents have railed against it, fearing it will not do enough to stop Iran getting the bomb.
Saudi Arabia -- leading an Arab coalition which today carried out a fifth straight night of air strikes on Iran-backed rebels in Yemen -- is also uneasy about any thawing in US-Iran ties.
Israeli Prime Minister Benjamin Netanyahu, in his second broadside in two days, said Monday a deal would be tantamount to Tehran being "rewarded" for its "aggression" in Yemen.
Western diplomats say some areas in a highly complex jigsaw puzzle are tentatively agreed. But they caution there is a long way to go.