If the talks in Moscow collapse, financial markets could grow increasingly nervous over the threats of higher oil prices and new conflict in the Middle East.
The United States, Russia, China, Britain, France and Germany want Tehran to curb its nuclear work and to stop enriching uranium to levels that bring it close to acquiring weapons-grade material.
Iranian negotiators want relief from economic sanctions and are pushing the six powers to acknowledge its right to enrich uranium, something they refuse to do until Tehran allows United Nations inspections of its work.
Deputy Foreign Minister Sergei Ryabkov, who leads Russia's delegation at the talks, said diplomacy could still be salvaged.
"I don't think anything will break down. We will have a reasonable outcome," Ryabkov told Reuters after meeting his counterparts from the six powers in a Moscow hotel on Tuesday.
He had called the two sides' negotiating positions "rather difficult and tough to reconcile" on Monday.
A spokesman for the head of the delegation talking to Iran also held out hope for a result on the second, final day.
"We had an intense and tough exchange of views," said a spokesman for European Union foreign policy chief Catherine Ashton. "We agreed to reflect overnight on each others' positions."
The Moscow talks follow two rounds of negotiations since diplomacy resumed in April after a 15-month hiatus during which the West cranked up sanctions pressure and Israel repeated its threat to bomb Iranian nuclear sites if diplomacy failed to stop Tehran getting the bomb.
"We haven't reached an agreement but it is more complex than that. We haven't got to the end of the conversation," said one Western diplomat present at the talks in the Russian capital.
A series of United Nations Security Council resolutions since 2006 have demanded Iran suspend all its enrichment-related activities. Tehran denies planning to build nuclear weapons and says its program is purely for civilian purposes.
Rather than halt enrichment - a process which refines uranium for use as fuel or, if done to a much higher level, nuclear bomb material - Iran has increased its activities.
SLIM HOPES OF BREAKTHROUGH
Experts said a breakthrough was unlikely, with the six powers - known as P5+1 because the group consists of the five members of the U.N. Security Council plus Germany - wary of making concessions that would let Tehran draw out the talks and gain the time needed to develop nuclear weapons capability.
An Iranian diplomat said on Monday: "Up to now the environment is not positive at all."
An EU embargo on Iranian oil takes full effect on July 1 and new U.S. financial sanctions some days before that. Iran's crude oil exports have fallen by some 40 percent this year, according to the International Energy Agency.
Increasing the pressure, Israel - widely believed to be the only nuclear-armed country in the Middle East - has said time is running out before Iran's nuclear facilities, some of which are deep underground, become invulnerable to air strikes.
Western diplomats said one positive sign to emerge from Monday's talks was that Tehran was willing to discuss their most pressing concern: higher-grade uranium.
In early 2010, Iran announced it had started enriching uranium to 20 percent purity, a level much higher than what is needed for power generation and seen by some experts as a dangerous step towards being able to make bomb material.
"They were very overt, more than they have ever been, in talking about 20 percent (fissile purity uranium) in a detailed and frank way," one Western diplomat said.
The six powers want a substantive response to their offer of fuel supplies for Tehran's research reactor and relief in sanctions on the sale of commercial aircraft parts to Iran.
At the last talks, in Baghdad in May, they asked Tehran in return to stop producing higher-grade uranium, ship any stockpile out of the country and close down an underground enrichment facility, Fordow.
Mistrust of Iran remains high. The International Atomic Energy Agency failed to persuade Iran, in talks this month, to let it inspect the Parchin military site where it suspects nuclear bomb-related research has taken place.