No final deal is expected at the two-day session.
However, if the Iranians succeed in building trust, the talks including the U.S., Britain, France, Russia, China and Germany could be the launching pad for a deal that has proven elusive since negotiations on Iran's nuclear program began in 2003.
That would reduce the threat of war between Iran and Israel and possibly the United States. The latter two have vowed never to accept a nuclear-armed Iran.
From the six-power perspective, the ideal outcome would be for Tehran to scale back aspects of its nuclear program that many nations fear could aid in making a bomb. That would trigger a gradual lifting of the economic sanctions on Iran.
On the eve of the talks, a senior U.S. administration official said Washington was encouraged by Rouhani's more moderate tone and would be testing Tehran's intentions in the coming days.
But the official, who was not authorized to speak on the record and briefed reporters on condition of anonymity, said the United States would insist on confidence-building measures "that address our priority concerns."
Heading Iran's delegation at the talks is Iranian Foreign Minister Javad Zarif, a veteran, U.S.-educated diplomat who helped negotiate a cease-fire with Iraq 25 years ago. He says his country is ready to allow more intrusive international perusal of Tehran's nuclear program.
Other Iranian officials, meanwhile, say there is room to discuss international concerns about Iranian uranium enrichment to 20 percent a level that is higher than most reactors use for power and only a technical step away from weapons-grade uranium suitable for warheads.
Iran now has nearly 200 kilograms (440 pounds) of 20 percent-enriched uranium in a form that can be quickly upgraded for weapons use, according to the U.N's atomic agency, which keeps tabs on Iran's nuclear activities. That is close to but still below what is needed for one nuclear weapon.
Even if Iran agrees to stop 20-percent production, ship out its 20-percent stockpile and allow more oversight by U.N. nuclear inspectors, the six powers want more.
A former senior U.N. official who has acted as an intermediary between U.S. and Iranian officials said the six powers want significant cuts in the more than 10,000 centrifuges now enriching uranium.
They also demand that Iran ship out not only the small amount of 20 percent uranium it now has but also most of the tons of low-enriched uranium it has produced. And they want caps on the amount of enriched uranium that Iran would be allowed to keep at any time. The official spoke on condition of anonymity because he was not authorized to comment on the talks.
Iran says it needs this material to power a future reactor network, and Iranian state television Sunday quoted Araghchi as saying Tehran was ready to discuss its enrichment program but would never ship enriched materials abroad. He described that stance as "our red line."
For the U.S. and its allies, low-enriched uranium is problematic because it can also be used to arm nuclear weapons, albeit the process is longer and more complicated than for 20 percent uranium.
While seeking only to reduce enrichment at a sprawling underground facility at Natanz, the six powers also want complete closure of another enrichment plant at Fordosouth of Tehran. The Fordo site is heavily fortified, making it more difficult to destroy than Natanz if it turns toward making nuclear weapons.
Demands to reduce enrichment instead of stopping it implicitly recognize Iran's right to enrich for peaceful purposes. That already is a victory for Tehran, considering talks began 10 years ago with the international community calling on the Islamic Republic to mothball its enrichment program.
"It's pretty clear that Iran will have to be allowed some degree of enrichment," said former U.S. State Department official Mark Fitzpatrick, who now is a director at the International Institute for Strategic Studies."But the enrichment has to be limited."
That could be a tough sell politically in the U.S. and Israel.
In a letter to President Barack Obama, 10 leading U.S. senators six Democrats and four Republicans insisted that Iran must end all uranium enrichment. Israeli Prime Minister Benjamin Netanyahu told his parliament Monday that the international community must maintain firm pressure on Iran until it quits enriching uranium.
The former U.N. official also said that his talks with senior Iranian officials indicate there will be tough bargaining on centrifuge numbers.
Even if Tehran agrees to downsize enrichment, the Iranians will probably offer stiff resistance to closing Fordo, he added summarizing his talks with senior Iranian officials directly involved in the upcoming negotiations.
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Associated Press Vienna bureau chief George Jahn has covered Iran's nuclear program since 2003.