"We hope that an agreement can be reached," said White House spokesman Jay Carney.
"The Iranians decided they were not able come to an agreement in the previous round, but we remain hopeful that we can reach an agreement with all of our P-5 plus one allies and the Iranians in Geneva," he said.
Carney said the White House was not reading out the Geneva negotiations "hour by hour or day by day."
"But we believe that the first round provided progress that indicated that it is at least possible to reach an agreement on this first phase," he said.
The spokesman's comments came amid upbeat reports from Geneva, where Iranian negotiators said progress was being made in the talks, now in their third day.
Russia's Foreign Minister Sergei Lavrov flew to Geneva, in a fresh push to clinch a deal.
"Last night we were a long way from foreign ministers coming. Today it has got closer," Iran's Foreign Minister Mohammad Javad Zarif said, according to the ISNA news agency.
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