The husband of a British woman jailed in Iran said he hopes to meet Boris Johnson "as soon as possible".
Iran's state TV broadcast a report claiming the Foreign Secretary's comments in Parliament about Nazanin Zaghari-Ratcliffe amounted to an "unintended admission" of her guilt.
The Channel 2 report said Mr Johnson's suggestion that Mrs Zaghari-Ratcliffe was "training journalists" when arrested in Iran last year had "dealt a blow" to the efforts of campaigners and UK authorities to support her position that she was in fact on holiday.
Mr Johnson has admitted that his comments "could have been clearer", and told MPs on Tuesday that the UK Government "has no doubt that she was on holiday" in Iran.
Mrs Zaghari-Ratcliffe's husband, Richard Ratcliffe, said he wants to meet Mr Johnson this week and has requested that he join the Foreign Secretary on a future trip to Iran.
Mr Ratcliffe, who said he has yet to speak directly to Mr Johnson, said the Foreign Secretary's office made contact with him on Friday.
"I think it's important now that he tries to meet with us as soon as possible, like next week, so that it's clear from a political point of view that the UK Government is standing alongside Nazanin and her family," Mr Ratcliffe told BBC Breakfast.
He added: "I think it'll happen now, in a way that two weeks ago I wasn't so sure. I think it's really important that he gets on a plane to go and see Nazanin. I'd really like to go with him and that's a serious request I've put to the Foreign Office."
Mr Ratcliffe said he has been told his request is being looked at as "a serious consideration".
Following Mr Johnson's comments last week, Mrs Zaghari-Ratcliffe was summoned before an unscheduled court hearing at which she was threatened with the doubling of her five-year jail sentence.
Wednesday's TV broadcast said that the British media and authorities had spent the last year trying to emphasise Mrs Zaghari-Ratcliffe's innocence "until last week, the UK Foreign Secretary Boris Johnson utters a sentence that proves costly for the government of this country".
It added: "Just this one sentence from the Foreign Secretary was enough to deal a blow to all the attempts of the British media and authorities in the past few months ...
"It appears that the statement of Boris Johnson was an antidote to all the statements of various media and UK authorities who had been claiming in the past year and a half that Nazanin Zaghari-Ratcliffe had come to Iran for humanitarian reasons."
Mrs Zaghari-Ratcliffe's employers, the Thomson Reuters Foundation, issued a statement in response to the Iranian TV reports, reiterating that she had never taken part in the training of journalists.
The foundation's chief executive, Monique Villa, said: "Nazanin is not a human rights activist with Thomson Reuters Foundation. She is a project manager in our media development team.
"At the foundation, we don't do advocacy work: we are ruled by the Trust Principles of Thomson Reuters which impose freedom from bias, independence and impartial reporting.
"Nazanin has never been a journalist, hence could never have trained journalists."
Ms Villa confirmed that Mrs Zaghari-Ratcliffe had visited Lebanon, Georgia and Morocco as part of her work running the logistics of workshops for local journalists.
"None of these workshops were attended by Iranian journalists. Nazanin didn't have any role in delivering the trainings and had no say in evaluating the work produced by the journalists trained," she said.