Boris Johnson will urge Iran to free British-Iranian woman Nazanin Zaghari-Ratcliffe from jail when he visits Tehran.
The foreign secretary is expected to travel to Iran in the next few days.
Ms Zaghari-Ratcliffe has been in prison since April 2016 after being accused of spying. She denies the claim.
Supporters of the 38-year-old from London say that she recently had a health assessment to see if she was fit enough to remain in prison.
Mr Johnson's Tehran trip will see him raising the cases of other dual nationals being held in Iran.
He will also discuss British concerns over Iranian involvement in conflicts in the Middle East, especially in Syria and Yemen.
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In November Mr Johnson apologised in the Commons after telling a committee of MPs that Mrs Zaghari-Ratcliffe had been teaching journalism in Iran.
He retracted "any suggestion she was there in a professional capacity".
Critics complained that the foreign secretary's initial comments could lead to her five-year jail term being increased.
Mr Johnson met her husband, Richard Ratcliffe, in November to discuss calls for her to be provided with diplomatic protection.
Mr Ratcliffe told BBC News his wife was due back in court on Sunday to face possible new charges and it was important Mr Johnson would be in Iran around the same time to "make clear that he thinks Nazanin is innocent and should be home with her family".
He said: "I don't know if I'm expecting him to be able to unlock it all, and she comes out with him, but it can only be a good thing that he is there".
Mr Ratcliffe said he had wanted to accompany Mr Johnson but the Foreign Office felt his presence would be "too political".
By James Landale, BBC diplomatic correspondent
When Boris Johnson arrives in Tehran this weekend, the foreign secretary will be required to perform some nifty diplomatic footwork even before he comes to address the case of Nazanin Zaghari-Ratcliffe.
For relations between Britain and the Islamic Republic of Iran are delicate at the best of times.
It is only six years since a mob stormed and sacked Britain's embassy in Tehran.
And to some in Iran, Britain will always be seen as the "Little Satan", a former imperial power that meddles in their country's affairs at America's bidding.
Both the UK and Iran have now restored diplomatic relations. But good relations are a work in progress.
So this visit, Mr Johnson's first, is designed above all to stabilise what has at times been a difficult relationship, a trip that was planned long before the case of Mrs Zaghari-Ratcliffe became a frontline political issue.
The mother had been visiting Iran with her daughter Gabriella when she was arrested last year.
The child has been living with her maternal grandparents in Iran for the last 20 months.
Mr Ratcliffe has not seen his daughter during his wife's incarceration.
There were concerns about Mrs Zaghari-Ratcliffe's health after lumps in her breasts were discovered but those were found to be non-cancerous.
In November Mr Ratcliffe said: "She talks about being on the verge of a nervous breakdown. I absolutely believe that's true.
"I think it's important I don't exaggerate anything in the media and I'm not melodramatic, but she is in a difficult place."