Boris Johnson will meet Iran’s President Hassan Rouhani on his second day of talks in the country.
The UK foreign secretary will continue to press for the release of Nazanin Zaghari-Ratcliffe, who has been held in Tehran since April 2016.
BBC diplomatic correspondent James Robbins says she faces a possible court appearance later on new charges.
On Saturday, Mr Johnson held “frank” talks within his Iranian counterpart for two hours on a range of subjects.
During the meeting with Mohammed Javad Zarif, he urged the release of Mrs Zaghari-Ratcliffe on humanitarian grounds, along with other dual nationals held in Iran.
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 our correspondent 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 baby daughter Gabriella and accused of spying – which she denies.
After the arrest, her daughter’s passport was confiscated and for the last 20 months she has been living with her maternal grandparents in Iran.
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”.
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 “charm and 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.”
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.
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.
In Saturday’s discussions, the nuclear deal from 2015 was raised following threats to scrap it from US President Donald Trump.
James Robbins said Iran credits Britain with sticking by the nuclear agreement, but it stressed “continuing disappointment” at the reluctance of banks and businesses to re-engage on the scale that French and German ones have.