Speaking in Paris earlier, Kerry said that together with British counterpart Philip Hammond -- who yesterday said he was "not optimistic" -- he was "concerned about the gaps".
"We all are," Kerry said.
Hammond had also suggested that the best hope was making enough progress to extend the deadline for a second time after an earlier cut-off point of July 20 was missed.
But Kerry, due to meet Iranian Foreign Minister Mohammad Javad Zarif this evening, said the parties "are not discussing an extension. We are negotiating to have an agreement."
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Such a deal, after 12 years of rising tensions, is aimed at easing fears that Tehran will develop nuclear weapons under the guise of its civilian activities -- an ambition the Islamic republic has always hotly denied.
Russia's main negotiator in the talks, Sergei Ryabkov, said tosday that the talks were being held in a "tense atmosphere" and that agreeing the mammoth accord would be tough.
"In the current situation it will be very difficult to get a deal unless there is a new spirit," Ryabkov was quoted as saying by Russian agency RIA Novosti.
Some areas appear provisionally settled in what would be a highly complex deal that would run for many years, even decades.
But two key issues remain: enrichment -- rendering uranium suitable for peaceful uses but also, at high purities, for a weapon -- and the pace of the lifting of sanctions.