The foreign secretary and the US secretary of state head to Geneva amid growing optimism that a deal on Iran’s nuclear programme is close to being struck.
Mr Hague told reporters there were narrow but important gaps between Iran and the six world powers from the E3+3 group involved in the talks, and negotiations remain “very difficult”.
Iranian Foreign Minister Mohammad Javad Zarif and Catherine Ashton, the European Union’s top diplomat, have held a series of talks since Wednesday, and have made progress on key areas, according to diplomats.
Mr Zarif has indicated that Iran is ready to sign up to an agreement without demanding that the international community acknowledges its “right” to enrich uranium, a big sticking point in the past.
Mr Kerry arrived in Geneva on Saturday, joining French foreign minister Laurent Fabius, and his Russian counterpart Sergey Lavrov. Mr Hague and his opposite numbers from Germany and China are all set to attend the talks.
A senior European diplomat told reporters earlier that foreign ministers of the six states would come to Geneva only if there was an agreement ready to sign.
Mr Hague said: “We have come now to support these negotiations and be able to confer together easily and quickly if we need to make fresh decisions of any kind.
“They remain very difficult negotiations, I think it’s important to stress that. We’re not here because things are necessarily finished, we’re here because they’re difficult and they remain difficult.
“There are narrow gaps but they are important gaps. It’s very important that any agreement is thorough, that it is detailed, that it is comprehensive, and that it is a deal in which we can all – the whole world – have confidence that it can work and it will be observed.”
He added: “We will only make a deal – the six countries involved – will only make an agreement if we think it is a truly worthwhile agreement and really does address the problems caused by Iran’s nuclear programme.”
A state department spokeswoman said Mr Kerry left for Switzerland “with the goal of continuing to help narrow the differences and move closer to an agreement”.
China’s state-run Xinhua news agency quoted a foreign ministry spokesman as saying the talks “have reached the final moment”.
The US and other western powers say there is no such thing under the nuclear Non-Proliferation Treaty as a “right to enrich”, but Iran has long viewed this as a matter of national sovereignty and a vital precursor to any deal.
Diplomats said the wording of a proposed new deal did not explicitly recognise a right to produce nuclear fuel by any country, but acknowledges all nations’ right to their own civilian nuclear energy programme.
Russian Deputy Foreign Minister Sergei Ryabkov said Iran’s demand to continue construction of a heavy-water reactor near Arak that could, when yield weapons-grade plutonium remained one of the main outstanding issues.
He told the Itar-Tass news agency: “Unfortunately I can’t say that there is a certainty of reaching that breakthrough.”
Iranian Deputy Foreign Minister Abbar Araqchi said: “We are close to a deal but still differences over two-three issues remain.”
The six powers want to cap Iran’s nuclear energy programme, which has a history of evading UN inspections and investigations, to remove any risk of refining uranium to a level suitable for bombs rather than electricity.
The draft deal would see Iran suspend nuclear activities above all medium-level enrichment in exchange for the release of billions of dollars in funds frozen in foreign bank accounts, and renewed trade in precious metals, petrochemicals and aircraft parts.
The US might also agree to relax pressure on other countries not to buy Iranian oil.