Boris Johnson and the President of Iran have "agreed on the need to make progress in all areas" following over an hour of talks.
The British foreign secretary met with Hassan Rouhani on Sunday, where the Foreign Office says they "spoke forthrightly...on a full range of regional and bilateral issues, including...the consular cases of dual nationals."
An FCO spokesman said: "After meeting Dr [Ali Akbar] Salehi, head of Iran's Atomic Energy Association, the Foreign Secretary concluded his visit to Iran with a meeting with President Rouhani.
"In both meetings the Foreign Secretary discussed the full range of regional and bilateral issues, including banking matters and our concerns about the consular cases of dual nationals.
"We leave with a sense that both sides want to keep up the momentum to resolve the difficult issues in the bilateral relationship and preserve the nuclear deal."
Mr Johnson also held "frank" discussions in Tehran on Saturday with his Iranian counterpart, Mohammad Javad Zarif, which was described as a "constructive" meeting.
The invitation to see Mr Rouhani was seen as a positive development given the often testy state of relations between the two countries.
It came as it remained unclear whether Mrs Zaghari-Ratcliffe would be taken back to court on Sunday following threats to increase her sentence by five years after Mr Johnson incorrectly told a parliamentary committee that she had been in Iran to train journalists.
Mother-of-one Mrs Zaghari-Ratcliffe was arrested in 2016 during a holiday visit to show her baby daughter Gabriella to her parents.
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Mrs Zaghari-Ratcliffe is serving a five-year sentence over allegations, which she denies, of plotting to overthrow the Tehran government.
Mr Johnson has been seeking her release during a two-day visit to Iran.
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The imprisoned woman's husband, Richard Ratcliffe, expressed concern at the prospect of his wife going to court again.
He told the Press Association: "I am obviously watching closely with hope, fingers crossed."
Mr Ratcliffe said he hoped the Foreign Secretary's visit would do some good.
"Hopefully, he will be persuasive and charming, and build a good relationship. It is definitely good that he is there, but let's wait and see what happens."
Tehran does not recognise Mrs Zaghari-Ratcliffe's dual UK-Iranian nationality, and refuses access to her for representatives of the British authorities, making a prison visit for the Foreign Secretary unlikely during the trip.
Mrs Zaghari-Ratcliffe's case is one of a small number of cases of dual nationals whose release Britain is seeking on humanitarian grounds on which Mr Johnson will push for progress.
Mr Johnson's trip to Tehran is only the third by a UK foreign secretary since 2003.
Additional reporting by Press Association
