Nazanin Zaghari-Ratcliffe will has had her prison furlough extended for two weeks, and will not now have to return to captivity until April 18.
The furlough – a temporary release – was granted as Iran came to terms with the coronavirus epidemic and had been expected to end on April 4.
But this weekend Richard Ratcliffe said his wife’s father had been told of the extension.
Richard also said his wife’s file has been put forward to the Iranian Prosecutor General to be considered for clemency.
The British-Iranian woman from West Hampstead has been living in relative isolation at her parents’ house in Tehran.
She has to wear an ankle tag during the furlough, and can only go within a 300-metre range of her parents’ home.
Iran is among the countries worst-affected by Covid-19 - reporting over 29,000 confirmed cases and more than 2,200 deaths from the disease.
The family’s MP Tulip Siddiq tweeted that every day Mrs Zaghari-Ratcliffe is out of prison is “better than the alternative”.
But she said the main focus remained “getting her home and away from the danger of coronavirus in Iran as soon as possible”.
Amnesty International UK director Kate Allen said: “”This is obviously better than being returned to the horrors of Evin Prison and we’re cautiously hopefully that now - finally - we could be getting to the end of the tunnel.
“Nazanin is a prisoner of conscience, convicted after a deeply unfair trial who should never have been behind bars at all.
“We’re once again calling on the Iranian authorities to end Nazanin’s ordeal and finally allow her to return to her family in the UK, as soon as she’s well enough to travel and as soon as any coronavirus travel restrictions allow.”
Former foreign secretary Jeremy Hunt welcomed the news on Twitter - calling it a “glimmer of hope amidst the darkness”.
“Let’s pray that this remarkable family are reunited soon,” he added.
Nazanin was arrested at Tehran’s Imam Khomeini airport while travelling to show her young daughter, Gabriella, to her parents in April 2016.
She was sentenced to five years in prison over allegations, which she denies, of plotting to overthrow the Tehran government.
She was later afforded diplomatic protection by the UK Government, which argues that she is innocent and that her treatment by Iran failed to meet obligations under international law.
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