One of Kerry's goals in prolonging an overseas trip to visit Vienna was "to have in-depth discussions" with Iranian Foreign Minister Mohammad Javad Zarif and "to gauge Iran's willingness to make the critical choices it needs to make," a senior State Department official said.
"That's a pretty serious and potentially lengthy conversation."
With just six days until Sunday's July 20 deadline to strike a deal, the differences appear considerable.
Iran denies seeking the atomic bomb and wants the lifting of all UN and Western sanctions, which have crippled its economy.
Without making any predictions, the State Department official said Kerry would "take the time necessary... To see if progress can be made."
The five permanent members of the UN Security Council plus Germany have been negotiating almost non-stop for months, after sealing an interim accord in November under which Iran froze its uranium enrichment in return for about USD 7 billion in sanctions relief.
Both sides are also under intense domestic pressure.
Beyond the negotiating table in Vienna, Zarif will have to come up with a deal that satisfies Iran's hardline Islamic leaders, while Kerry is under pressure from Congress ahead of November mid-term elections not to concede too much to Washington's traditional foe.
The United States and Iran have not held diplomatic ties for three decades, making the face-to-face talks between the two top diplomats all the more remarkable.
But Germany's Foreign Minister Frank-Walter Steinmeier, who like his other counterparts from Britain and France held one-on-one talks with Zarif yesterday in Vienna, was the most pessimistic warning that "the ball is in Iran's court".
"It is now up to Iran to decide to take the path of cooperation... I hope that the days left will be enough to create some reflection in Tehran," he said.
Britain's Foreign Secretary William Hague said there had been no "decisive breakthrough" and a "huge gap" remained on the key issue of uranium enrichment.
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