The differences preventing Western countries reaching a deal with Iran over its nuclear programme are now "narrow", William Hague has said.
The UK foreign secretary added that, although talks at the weekend had not resulted in agreement, some "gaps" had been "bridged altogether".
Iran and the UK have announced that diplomatic visits between the countries will take place later this month.
Sanctions would remain in place until a firm deal was in place, Mr Hague said.
His statement to the House of Commons came after US Secretary of State John Kerry said Iran had backed out of a deal to freeze expansion of its nuclear activity in return for limited relief from international sanctions.
The Geneva talks involved Iran and the P5+1: the US, Russia, the UK, France and China as permanent UN Security Council members, plus Germany.
Mr Hague told MPs the aim was to produce an interim agreement before moving on to a fuller deal, but that "some differences" between the parties remained after discussions on Friday and Saturday.
However, he added: "Most of these gaps are now narrow and many others were bridged altogether during the discussions."
Mr Hague said he was confident of further progress at the next round of meetings, starting on 20 November, and there had been "a substantial step towards a comprehensive settlement".
Sanctions against Iran were causing its economy to lose $4bn a month and would remain in place until a full agreement, he added.
Mr Hague also said: "We are determined to reach a diplomatic settlement to the Iran nuclear crisis."
Iran and the UK agreed to renew direct diplomatic links during talks over the state's nuclear ambitions last month.
The UK's new charge d'affaires for Iran, Ajay Sharma, was named on Monday. He is expected to visit the country later this month, as efforts to improve relations continue.
Iran has also named its charge d'affaires, Mohammad Hassan Habibollah, who will come London "in the near future to examine the situation of Iran's possessions and buildings in Britain and to improve consular activities", according to the foreign ministry.
Mr Sharma, former head of the Foreign Office's Iran department, said: "I am delighted to take up this appointment at this important time in the UK's relations with Iran. I am very much looking forward to renewing direct UK contact with the Iranian government and society.
"This is very much in the interests of both our countries. I hope to make my first visit to Tehran as non-resident charge later this month."
The UK shut down its Tehran embassy in 2011 after it was stormed in a protest over sanctions imposed because of its nuclear programme.
Iran says its uranium-enrichment is for energy-creation purposes, rather then weapons.
Significant progress is believed to have been made on a deal after Hassan Rouhani, perceived as a moderate, was elected president this summer, despite the weekend's disappointments.
Asked about the prospects of agreement, Prime Minister David Cameron's spokesman said "it can be done", despite requiring "formidably difficult negotiation".