Iran and six world powers were closing in on a long-elusive deal aimed at allaying international fears about Tehran's nuclear ambitions.
After the first day of a two-day meeting, they said progress had been made towards an agreement under which Iran would curb some of its nuclear activities in exchange for limited relief from sanctions.
Negotiators cautioned, however, that work remained to be done in in very complex negotiations and that a successful outcome was not guaranteed.
Iran rejects Western accusations that it is seeking the capability to make nuclear weapons.
Iranian Deputy Foreign Minister Abbas Araqchi said it was too early to say with certainty whether a deal would be possible this week, though he voiced cautious optimism.
The United States and its allies are aiming for a "first step" deal that would stop Iran from further expanding a nuclear programme that it has steadily built up in defiance of tightening international pressure.
US Secretary of State John Kerry is to travel to Geneva tomorrow at the invitation of European Union foreign policy chief Catherine Ashton in an effort to help narrow differences in negotiations, a senior US official said.
The Islamic Republic, which holds some of the world's largest oil and gas reserves, wants them to lift increasingly tough punitive measures that have slashed its daily crude sales revenue by 60% in the last two years.
Both sides have limited room to manoeuvre, as hardliners in Tehran and Washington would likely sharply criticise any agreement they believed went too far in offering concessions to the other side.
Lending urgency to the need for a breakthrough soon, a US Senate committee said it would pursue a package of tough new sanctions on Iran after the current Geneva talks end tomorrow.
President Barack Obama has been pushing Congress to hold off on more sanctions against Iran, demanded by Israel, to avoid undermining the diplomacy aimed at defusing fears of an Iranian advance towards nuclear arms capability.
A spokesman for the European Union foreign policy chief Catherine Ashton - who is presiding over the talks - said this evening that the powers and Iran were "making progress" towards easing the decade-long standoff.
Ms Ashton is due to meet Iran's foreign minister and chief negotiator, Mohammad Javad Zarif, tomorrow morning "to allow more time to work through some issues".
Iran says it is enriching uranium only to fuel future nuclear power stations and for medical purposes.
But its refusal to halt activity which can also have military applications has drawn the increasingly tough sanctions.
The United States said it also held "substantive and serious" bilateral talks with Iran in Geneva.
White House spokesman Jay Carney said that in exchange for "concrete, verifiable measures" of restraint by Iran, the six powers "would consider limited, targeted, and reversible relief that does not affect our core sanctions architecture".
The broader sanctions regime would stay pending a "final, comprehensive, verifiable" accord, Mr Carney told reporters in Washington.
If Iran did not follow through towards this end, modest sanctions relief could be reversed and stiffer penalties imposed.