Kerry and Hague will take part in the push to seal an interim deal between Iran and world powers on Tehran's nuclear program.
Hague told reporters, "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."
The new developments came as Iranian Foreign Minister Mohammad Javad Zarif and European Union foreign policy chief Catherine Ashton held a new meeting on the eve of the fourth day of the talks.
Iran and the five permanent members of the United Nations Security Council -- the United States, France, Britain, Russia and China -- plus Germany kicked off their latest round of talks on Wednesday.
Russian Foreign Minister Sergei Lavrov also arrived in the Swiss city on Friday afternoon and held a meeting with Zarif and later with Ashton.
Chinese Foreign Minister Wang Yi will also head to Geneva to join the negotiations as the talks extend to a fourth day.
Hopes are now rising that a final deal that many say could end the West's standoff over the Iranian nuclear energy program is just around the corner.
The Iranian delegation has been engaged with one-on-one meetings with other delegations to hammer out an interim deal to pave the ground for the resolution of the West’s decade-old standoff with Iran over its nuclear energy program.
“To a good degree, we have moved (closer) towards agreement,” Iranian Deputy Foreign Minister Seyyed Abbas Araqchi said late on Friday, adding however that "some main issues still remain."
Meanwhile, IRNA news agency quoted an unnamed Western diplomat as saying that the six world powers have accepted the Islamic Republic’s right to enrich uranium.
RA/SHI