EU foreign policy chief Catherine Ashton told a press conference that there had been a lot of “concrete progress but some differences remain”.
Baroness Catherine Ashton said talks would resume on November 20.
Iranian Foreign Minister Mohammad Javad Zarif said he was not disappointed with the outcome, and that the talks were “something we can build on”.
Mohammad Javad Zarif said all parties were “on the same wavelength” and “there was the impetus to reach an agreement”.
Meanwhile US Secretary of State John Kerry said: “There is no question in my mind that we are closer now than we were before.”
The international powers are concerned that Tehran is trying to build a nuclear weapon – but Iran says its programme is peaceful.
A proposal that was floated would require Iran to freeze expansion of nuclear activity in return for limited relief from economic sanctions.
Delegates had earlier suggested there was “good progress”.
But diplomatic sources said France had wanted tougher terms for Iran.
Before the late-night press conference, French Foreign Minister Laurent Fabius said the three days of negotiations had ended without a deal.
“The meetings in Geneva have made it possible to move forward,” he said.
“But we have not yet managed to conclude, because there are still some questions remaining to be dealt with.”
Meanwhile, John Kerry told reporters: “We have not only narrowed differences and clarified those that remain but we made significant progress in working through the approaches to this question of how one reins in a programme and guarantees its peaceful nature.”
He added that the window for diplomacy would not stay open indefinitely.
Iranian President Hassan Rouhani had urged the world powers not to miss an “exceptional opportunity” to seal an agreement.
The Geneva talks involve Iran and the P5+1 (the US, Russia, Britain, France and China as permanent UN Security Council members, plus Germany).
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