Amid signs that the talks in Geneva were proving difficult, Kerry's spokesman said the US's top diplomat would leave for London on Sunday for meetings with British counterpart William Hague and the Libyan prime minister.
At the same time, Iranian chief negotiator Abbas Araqchi said he doubted that Tehran and the P5+1 world powers — comprising the United States, Britain, France, China, Russia and Germany — could reach an accord by the end of the day.
"Intense and difficult negotiations are under way and it is not clear whether we reach an agreement tonight," Fars news agency quoted Araqchi as saying.
"The dispute is over the wording."
The talks are aimed at securing a freeze on parts of Iran's nuclear programme in order to ease fears that Tehran will develop atomic weapons, in return for modest sanctions relief.
The arrival of foreign ministers including Kerry on Saturday had raised hopes, after three days of intense negotiations among lower-level officials, that a breakthrough was in sight.
Kerry had decided to join the talks "with the hope that an agreement will be reached," the State Department said on Friday.
Since their arrival however, officials from both sides have indicated that there are still considerable differences to be bridged.
"We have now entered a very difficult stage," Iranian Foreign Minister Mohammad Javad Zarif told state television, saying he would not bow to "excessive demands".
"In any agreement, (uranium) enrichment in Iran will not be suspended," Zarif said, adding that "a very difficult task" still lay ahead in clinching a deal.
Hague was also cautious on Saturday morning.
"They remain very difficult negotiations," he said in Geneva.
"I think it is important to stress that we are not here because things are necessarily finished."
"It's not a done deal," said his German counterpart Guido Westerwelle.
"We think there's a realistic chance but there is still a lot of work to do."
Mark Hibbs from the Carnegie Endowment for International Peace said Kerry's imminent departure might "set a deadline and focus people's minds".
Just two weeks ago, the ministers had jetted in seeking to sign on the dotted line, only to fail as cracks appeared among the powers — fissures that officials say are now repaired.
Since being elected in June, Iranian President Hassan Rouhani has raised big hopes that after a decade of rising tensions over Tehran's nuclear programme, a solution might be within reach.
Devil in the detail
Iran insists its nuclear programme is peaceful but many in the international community suspect it is aimed at acquiring atomic weapons.
The six powers want Iran to stop spinning, for six months initially, some 700 of its some 19,000 thousand centrifuges that are enriching uranium to levels close to weapons-grade.
They also want Tehran to stop constructing a new reactor at Arak and to grant the International Atomic Energy Agency more intrusive inspection rights.
In return they are offering Iran minor and reversible relief from painful sanctions including unlocking several billion dollars in oil revenues and easing some trade restrictions.
Ministers in Geneva are seeking to obtain a "first phase" deal which would build trust and ease tensions while negotiators push on for a final accord that ends once and for all fears that Tehran will acquire an atomic bomb.
A major sticking point has been Iran's demand — as expressed by supreme leader Ayatollah Ali Khamenei this week — for recognition of its "right" to enrich uranium.
The risks posed by failure are high: Tehran could resume the expansion of its nuclear activities, leading to more painful sanctions and even Israeli and possibly US military action.
A hard sell
Getting an agreement palatable to hardliners both in the United States and in the Islamic republic — as well as Israel — is tough.
Israeli Prime Minister Netanyahu wants all of Iran's nuclear infrastructure dismantled, not just parts of it frozen, believing that the P5+1 will leave Iran with an ability to develop nuclear weapons.
In Washington there is a push by lawmakers to ignore President Barack Obama's pleas and pass yet more sanctions on Iran if there is no deal — or one seen as too soft.
Rouhani, meanwhile, is under pressure to show Khamenei the first fruits of his "charm offensive", and it is unclear whether the sanctions relief on offer is enough.