"We will now move to the next phase in the negotiations in which we will aim to bridge the gaps in all the key areas and work on the concrete elements of a possible comprehensive agreement," said EU foreign policy chief Catherine Ashton who is the chief negotiator for the world powers.
In a statement repeated in Farsi by Iran's foreign minister Mohammad Javad Zarif, Ashton said a "lot of intensive work will be required to overcome the differences which naturally still exist at this stage in the process."
The permanent council members are the United States, Russia, China, Britain and France.
The fourth and next round will be held in Vienna again from May 13, they said.
A senior US administration official involved in the talks had said last week that the negotiators hoped to make enough progress in this round to begin drafting a deal in May.
In November the two sides reached an interim deal under which Iran froze certain parts of its nuclear activities in return for minor relief from painful Western sanctions.
US Secretary of State John Kerry told US lawmakers Monday that the theoretical period needed for Iran to produce a weapon's worth of bomb material -- if it chose to do so -- was "about two months".
In order to greatly extend this "break-out" time, the six powers want the final deal to see Iran reduce permanently, or at least long-term, the scope of its programme.
The deal may involve Iran slashing the number of centrifuges -- used to enrich nuclear material -- changing the design of a new reactor at Arak and giving UN inspectors more oversight.
Iran's supreme leader Ayatollah Ali Khamenei said Wednesday "that Iran's activities in nuclear research and development as well as its nuclear achievements will never be stopped.
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