US Secretary of State John Kerry has said that the United States continues to be sceptical of Iran's willingness to dismantle its nuclear programme and will keep sanctions in place as talks continue.
Mr Kerry said: "I think we have a pretty strong sense of how to measure whether or not we are acting in the interests of our country and of the globe."
He said that the US is aiming to get Tehran to halt further nuclear development as a first step toward a complete dismantling of the programme.
Iran and six world powers failed in marathon talks to clinch a deal to curb Tehran's nuclear programme.
Negotiators have said that differences have narrowed and that negotiations would be resumed in 10 days in a fresh bid to end the decade-old standoff.
Clear divisions emerged among the US and European allies on the final day of the talks.
France hinted that the proposal under discussion did not sufficiently neutralise the threat of an Iranian nuclear bomb.
Iran is hoping for a deal that would ease the international sanctions that have frozen its assets around the world and prevented it from selling its oil.
It is ultimately the Americans and Iranians, who have not had formal diplomatic ties for more than three decades, who have the power to make or break an agreement.
But yesterday the attention suddenly turned to the French after Foreign Minister Laurent Fabius told France Inter radio that Paris could not accept a "fool's game" - in other words, a weak deal with Iran.
"From the start, France wanted an agreement to the important question of Iran's nuclear programme," Mr Fabius told reporters after the meeting, which ran into the early hours of this morning.
"The Geneva meeting allowed us to advance but we were not able to conclude because there are still some questions to be addressed," Mr Fabius said.
Mr Fabius' pointed remarks rankled others in the Western camp. One diplomat close to the negotiations said the French were trying to upstage the other powers and were causing unnecessary trouble for participants in the talks.
Ms Ashton and Iranian Foreign Minister Mohammad Javad Zarif said they hoped an agreement would be signed later this month.
"We have done some intense negotiations and discussions and our objective is to reach a conclusion and that's what we will come back to try and do," Ms Ashton said.
Mr Zarif said: "We had a very good three days, very productive three days, and it is something we can build on."