"We are continuing to negotiate for the next couple of days," EU foreign policy chief Federica Mogherini told reporters during a break in negotiations in Vienna.
But the United States said the terms of a November 2013 interim accord under which Iran has been cutting back its stock of enriched uranium in return for sanctions relief would be extended until Friday, July 10, meaning this is the effective new deadline.
Negotiators were taking the talks "day by day" as they seek to slot into place the last pieces of a complex negotiation which has lasted almost two years now to deny Iran a nuclear bomb in return for sanctions relief.
It was the fifth time since 2013 -- and the second time in this round of talks -- that negotiators have missed their own target date as talks have bogged down.
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US Secretary of State John Kerry is remaining in Vienna with Mogherini and their Iranian counterpart Mohammad Javad Zarif. Their Russian and Chinese counterparts had already left.
"I think there is a clear will on both sides now to complete this agreement and to keep at it until we get there," said British Foreign Secretary Philip Hammond before also flying home for 24 hours for budget talks.
After talking deep into the night Monday, foreign ministers from the so-called P5+1 -- Britain, China, France, Germany, Russia and the United States -- met three times today without their Iranian counterparts.
For many observers July 9 had always been the real deadline, and the US team now has its back against the wall trying to nail down the final details by then.
If Kerry fails to hand over a deal by late Thursday, US lawmakers will get 60 days instead 30 to review it, which risks further complicating its implementation.