Nazanin Zaghari-Ratcliffe, a project manager with the Thomson Reuters Foundation, was sentenced to five years after being convicted by an Iranian court of plotting to overthrow the Islamic Republic's clerical establishment.
It follows an apology by the foreign secretary for "anguish" caused by false remarks he made about the reason for her travels.
The Foreign Secretary is to meet Mr Ratcliffe tomorrow to discuss the possibility of his wife being offered "diplomatic protection" in an attempt to secure her freedom.
He continued: "I do apologise, I do apologise, and of course I retract any suggestion that she was there in a professional capacity". She was there on holiday.
Mr Johnson said: "Yes, of course, I apologise for the distress, the suffering that has been caused by the impression that I gave that the Government believed, that I believed, she was there in a professional capacity".
Iranian-British aid worker Nazanin Zaghari-Ratcliffe is seen in an undated photograph handed out by her family.
The Foreign Secretary told MPs on Monday there were "overwhelming" humanitarian grounds for her release and stressed that she was in Iran on holiday.
The Iranian state broadcaster said this amounted to an "unintended admission" of her guilt.
She claimed his recent comments to the foreign affairs select committee had made Mrs Zaghari-Ratcliffe's situation worse by suggesting that she had been there to train journalists. There are also fears she is developing cancer after finding lumps in her breasts.
Mrs Zaghari-Ratcliffe was arrested in April 2016 as she tried to leave Tehran with her young daughter Gabriella following a trip to see family in Iran.
Despite her family pleading for help from the Foreign Office for more than 18 months, Mr Johnson told the foreign affairs committee she had been training journalists in Iran - comments which the state broadcaster said amounted to an "unintended admission" of her guilt.
Ms Zaghari Ratcliffe has denied the charges. Some critics have called for Johnson to resign, but Ratcliffe said it would not be in his wife's best interests.
Mr Johnson has sought advice from officials to determine whether conferring the status could help, including what impact it would have on the support now being provided and the representations already being made on Ms Zaghari-Ratcliffe's behalf.
He said: 'She has been very angry for a number of days.
Mr Ratcliffe welcomed the opportunity to meet Mr Johnson in person, having only spoken to him over the phone.
'This is life or death.