UK Foreign Secretary Boris Johnson will meet Iran’s President Hassan Rouhani on a second day of talks in the country.
He will continue to press for the release of Nazanin Zaghari-Ratcliffe, who has been held since April 2016 on charges of spying, which she denies.
She faces a possible court appearance later on new charges.
On Saturday Mr Johnson urged his Iranian counterpart to release Mrs Zaghari-Ratcliffe and other dual nationals on humanitarian grounds.
Richard Ratcliffe, who has been campaigning for his wife’s release, said: “Hopefully he will be persuasive and charming and build a good relationship.”
In two hours of talks, Mr Johnson and Mohammed Javad Zarif also discussed “the obligations of all parties to implement the nuclear deal”, Iran’s foreign ministry said.
US President Donald Trump has made his opposition to the deal, struck in 2015, very clear and has threatened to scrap it. But the UK continues to support it. In October when Mr Trump threatened to tear the deal apart, the UK, France and Germany said it was “in our shared national security interest” that its arrangements continue.
BBC diplomatic correspondent James Robbins said the confirmation of Mr Johnson’s meeting with the president had “encouraged” the British delegation, as it is not automatic for Mr Rouhani to meet with a visiting foreign minister.
But he said the president’s powers were limited as he is not Iran’s supreme leader.
Mrs Zaghari-Ratcliffe was arrested on a visit to see her parents with her infant daughter Gabriella.
After the arrest, her daughter’s passport was confiscated and for the last 20 months the three-year-old has been living with her maternal grandparents in Iran.
Iran does not recognise Mrs Zaghari-Ratcliffe’s dual citizenship and will not allow UK representatives to see her in prison.
The case was further complicated when Mr Johnson erroneously told a parliamentary committee in November that Mrs Zaghari-Ratcliffe had been in Iran to train journalists.
The foreign secretary later apologised in the Commons, retracting “any suggestion she was there in a professional capacity”.
But she now faces new charges of spreading propaganda, which could double her sentence.
Last month, the Free Nazanin Campaign said Mrs Zaghari-Ratcliffe had suffered panic attacks, insomnia, bouts of depression and suicidal thoughts and had been given a health assessment.
Mr Ratcliffe said: “[Mr Johnson’s] fate and her fate have been aligned a little bit, and he is now in Iran battling for her. It’s a case of ‘watch this space'”.
He said he believed the foreign secretary’s presence in Iran would “make a difference”, but the situation remained very unclear.
“It’s all up in the air,” said Mr Ratcliffe. “We’re holding on to the good bits – it could go any which way.”
He said he wanted his wife to be with her family in the UK for Christmas but he was not expecting her to be on the plane when Mr Johnson returns to the UK on Monday.
He added: “Fingers crossed it can be solved by Christmas, which means in the week or so afterwards there might be a happy outcome.”
The Foreign Office would not confirm the names or number of other dual nationals being held, saying their families had asked for their cases to be kept out of the public domain.
Relations between the UK and Iran have long been difficult. Mr Johnson’s visit is only the third by a British foreign minister to Iran in the last 14 years.