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 UN Security Council plus Germany into a lasting accord by July.
Such an agreement -- seen as highly ambitious -- 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".
So far, even with differences over Syria, the six powers have shown a united front over Iran, but events in Ukraine in recent weeks have precipitated the worst crisis in East-West relations since the Cold War.
Following Sunday's referendum in Crimea -- slammed as illegal by the White House and the European Union -- Brussels and Washington on Monday slapped travel bans and asset freezes on top Russian and Ukrainian figures.
Already downbeat about prospects for a deal with Iran, Mark Fitzpatrick, a former US State Department official now at the London-based International Institute for Strategic Studies, said the spat made him "even more pessimistic".
"The Russians will ... be less likely to make sacrifices for the sake of unity over the Iran issues," Fitzpatrick told AFP. The Iranians, he said, "now have more reason to wait out the six powers".
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.
This would undermine Washington's efforts to cut off Iran's main source of revenue -- a strategy which the US credits with forcing Tehran to the negotiating table in the first place.
Mark Hibbs from the Carnegie Endowment for International Peace said this "huge barter deal" is a "carrot Moscow can dangle constructively to wrestle more concessions from Iran."
"Or it can move forward unilaterally and damage the negotiation," Hibbs told AFP. "Up to Putin to choose."
- Rubik's Cube -
Describing a deal with Iran as a "Rubik's Cube" puzzle, a senior US official said Friday 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, said Sunday 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 has not permanently dismantled a single piece of atomic equipment. The bulk of UN and Western sanctions remain in place, depriving Iran of billions of dollars in lost oil revenues every week.
The United States, China, Russia, Britain, France and Germany now want Iran to reduce permanently -- or at least for a long time -- the scope of its activities, as well as more intrusive UN inspections.
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," Vaez told AFP.