Johnson told a parliamentary committee last week that Nazanin Zaghari-Ratcliffe was training journalists in Iran when she was arrested for alleged sedition last year -- something her employer and her family insist is incorrect.
Zaghari-Ratcliffe appeared in court on Saturday to face further charges, brought in early October, that carry a 16- year jail term.
The Iranian judiciary issued an online article on Sunday saying that Johnson's comments proved that she wasn't on holiday, as claimed, backing the justification for new charges.
Johnson was due to call Iranian Foreign Minister Mohammad Javad Zarif today in a bid to defuse the situation.
Richard Ratcliffe, the detainee's husband, told AFP that Johnson "made a factual error, and then it felt more ominous on Sunday when that factual error was being used to justify her detention."
He said that Johnson's phone call to his Iranian counterpart was "not good enough" and that he needed to officially correct the record to send a message to Iran's judiciary.
He added that Saturday's court appearance had left his wife "very stressed and upset".
Zaghari-Ratcliffe, who works for the Thomson Reuters Foundation (TRF), the media organisation's philanthropic arm, was arrested at Tehran airport on April 3, 2016 after visiting family.
Iran's elite Revolutionary Guards accused her of having taken part in the "sedition movement" of protests that followed the disputed 2009 re-election of then hardline president Mahmoud Ahmadinejad. Zaghari-Ratcliffe denies the charges.
She is serving a five-year jail sentence in Tehran but last month was presented with extra charges carrying a possible 16-year prison term, her employers said.
Following Johnson's comments, TRF chief executive Monique Villa urged him to "immediately correct the serious mistake".
"She is not a journalist and has never trained journalists at the TRF where she is project manager," Villa said in a statement.
"She was in Iran on holiday to show her daughter Gabriella to her grandparents."
Emily Thornberry, foreign affairs spokeswoman for the main opposition Labour Party, wrote to Johnson urging him to quit if his actions have damaged Zaghari-Ratcliffe's prospects of freedom.
Britain's International Trade Secretary Liam Fox told Sky News television that he did not believe Johnson had made "a serious gaffe".
Fox said the situation was being used as an attempt to discredit Johnson without thinking of the possible consequences.
"The most important thing is to do what he's doing today: to make very clear to his Iranian counterpart that this would not be any excuse for extending an illegal detention," Fox also told BBC radio.
"We all make slips of the tongue. I think we've got to be very careful that we're not over-reacting to this.
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