Threatening to drive a wedge between the powers, however, is the crisis over Ukraine, which has led to the biggest standoff between Russia and the West since the Cold War.
Iran and the five UN Security Council permanent members plus Germany want to transform a temporary accord struck in November into a permanent agreement before it lapses on July 20.
Doing so is a tall order, however, requiring both sides to tackle thorny issues that will severely test their willingness and ability to give ground.
A spokesman for the powers' chief negotiator, EU foreign policy chief Catherine Ashton, said this round, expected to last two days, was to "explore our respective positions on each topic".
A senior US official involved in the talks said Friday she was "absolutely convinced" a deal could be reached and that both sides were "looking toward beginning drafting in May".
Under the November deal, which took effect on January 20, Iran froze certain nuclear activities for six months in exchange for minor relief from sanctions hurting its economy.
US Secretary of State John Kerry told US lawmakers yesterday that the theoretical period needed for Iran to produce a weapon's worth of bomb material -- if it chose to do so -- was "about two months".
In order to greatly extend this "break-out" time, the six powers want the final deal to see Iran reduce permanently, or at least long-term, the scope of its programme.
The deal may involve Iran slashing the number of centrifuges -- machines "enriching" nuclear material -- changing the design of a new reactor at Arak and giving UN inspectors more oversight.
If Iran gives away too much this risks losing Iranian President Hassan Rouhani -- who since taking office last year has sought to improve ties with the West -- the support of the supreme leader.
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