Iran's insistence that any agreement must allow its experts to carry out this process had been a key sticking point in the negotiations in Geneva.

Trita Parsi, president of the National Iranian American Council, said a way had been found to overcome this problem. Any agreement would not refer explicitly to enrichment, but to the nuclear non-proliferation treaty, which Iran interprets as giving it the right to use this technology. ''Both sides won,'' wrote Mr Parsi in an email.

However, there remains a second key dispute over a new plutonium reactor at Arak. The US and allies want Iran to stop building this facility, fearing that it could provide another route to a nuclear weapons capability.

Baroness Ashton, the European Union's high representative for foreign policy, was in talks with Mohammad Javad Zarif, the Iranian Foreign Minister, on the third day of talks.

A diplomat close to the negotiations predicted the meeting would continue into the weekend, adding all sides were concerned over ''how long the window will stay open - and how many times we can come back here''.

Washington said Mr Kerry's visit, the second in two weeks after he and other foreign ministers failed to agree an accord in earlier talks, was aimed at '''continuing to help narrow the differences and move closer to an agreement''.

French Foreign Minister Laurent Fabius was also set to join the talks, a French diplomatic source said, while British Foreign Secretary William Hague said on Twitter he would be there on Saturday.

Russian Foreign Minister Sergei Lavrov arrived in the Swiss city on Friday afternoon.

This third round of talks since Iranian President Hassan Rouhani's election in June is seen as the biggest hope to resolve the decade-old standoff over Iran's nuclear program, which world powers want halted but which Tehran insists is peaceful.

Failure might mean Iran resuming the expansion of its atomic activities, Washington and others adding to already painful sanctions, and possible Israeli and even US military action.

At the last three-day gathering from November 7-10, top diplomats including Mr Kerry flew in but went home empty-handed.

Both sides say they want a deal but getting an accord palatable to hardliners in the US and Iran - as well as Israel - is tough.

According to a draft proposal, the US, Britain, China, France, Russia, and Germany want Iran to freeze for six months key parts of its nuclear program. In return Iran would get minor and ''reversible'' sanctions relief, including unlocking several billion dollars in oil revenues and easing trade restrictions on precious metals and aircraft parts.

TELEGRAPH, AFP