"We have reached agreement between E3+3 and Iran," Ashton's spokesman Michael Mann quoted her as saying on Twitter, without giving any details.
Iranian Foreign Minister Mohammad Javad Zarif tweeted: "We have reached an agreement."
The announcement came after more than four days of talks in Geneva between Iran and the United States, China, Russia, Britain, France and Germany, chaired by Ashton, who is the European Union's top diplomat.
The talks were aimed at getting Iran to scale back parts of its nuclear programme in return for relief from painful sanctions imposed by the UN Security Council and Western countries.
Numerous diplomatic initiatives have failed over the past 10 years to persuade Iran to rein in its programme, which Tehran insists is peaceful but which Western countries suspect is aimed at crafting atomic weapons.
Foreign ministers from the six powers including US Secretary of State John Kerry had jetted into Geneva for the second time in two weeks on Saturday morning after negotiators made good progress.
Hopes they would quickly sew up the agreement faded however as the talks dragged on throughout Saturday and until the early hours of Sunday morning and the announcement at 3:00 am (0200 GMT).
It was unclear how this tricky issue has been got around in the new deal. Officials were due to give press conferences later today.
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