It is the second in a planned series of meetings this year that aims to transform a November interim deal between Iran and the five permanent members of the United Nations Security Council plus Germany into a lasting accord by July.
Such an agreement would put an end to a decade-old standoff over Iran's nuclear programme and silence for good what US President Barack Obama has called the "drums of war".
Following Sunday's referendum in Crimea, slammed as illegal by the White House and the European Union; Brussels and Washington had slapped travel bans and asset freezes on top Russian and Ukrainian figures yesterday.
Even before the Ukraine crisis erupted, Russian President Vladimir Putin was reported to be discussing a major deal with Iran whereby Moscow would buy Iranian oil in exchange for money, goods and help in building new nuclear reactors.
Describing a deal with Iran as a "Rubik's Cube" puzzle, a senior US official said last week that the parties were "moving forward in a positive way", although "many gaps" remained.
Iranian Foreign Minister Mohammad Javad Zarif, installed last year by Iran's relatively moderate new President Hassan Rouhani, had said on Sunday that the talks would be "more serious than previous ones".
Under November's agreement, Iran froze key parts of its nuclear programme in return for minor sanctions relief and a promise of no new sanctions. Although it could be extended, the deal is currently due to expire on July 20.
Iran, denying that it wants nuclear weapons, wants all sanctions lifted and its "right" to a peaceful nuclear programme recognised.
"The final agreement will fall short of both sides' ideals," said Ali Vaez, Iran expert at the International Crisis Group.
"The West will have to live with more Iranian centrifuges (for producing nuclear material) that it deems appropriate and Iran will have to accept less sanctions relief that it desires," he added.
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