Downing Street said the PM held a phone conversation with Hassan Rouhani on Wednesday.
Mr Johnson demanded Ms Zaghari-Ratcliffe’s immediate release, along with that of other British-Iranian dual nationals, Downing Street said.
Ms Zaghari-Ratcliffe was recently released from house arrest and had her ankle tag removed following a five-year prison term.
The Thomson Reuters Foundation worker was detained in 2016 on spying charges which she denied and the UK has also rejected.
A No 10 spokesperson said: “[Mr Johnson] said that while the removal of Nazanin Zaghari-Ratcliffe’s ankle monitor was welcome, her continued confinement remains completely unacceptable and she must be allowed to return to her family in the UK.”
It is feared that Ms Zaghari-Ratcliffe may face further charges, with a fresh court hearing expected on Sunday.
Her husband Richard Ratcliffe, accompanied by their six-year-old daughter Gabriella, attended a vigil outside the Iranian embassy in Knightsbridge, central London, on Monday.
Kate Allen, Amnesty International UK’s director, said: “Nazanin has already been convicted once after a deeply unfair trial before a revolutionary court, so of course we’re extremely concerned about this hearing.”
She said that Iran “systematically [violates] fair trial rights” and that it was vital British officials be granted permission to attend any court hearings.
Downing Street has previously said that officials have been denied access to legal proceedings because Iran does not recognise dual nationality.
The Foreign, Commonwealth and Development Office reiterated its displeasure at Iran’s imprisonment of dual nationals as “diplomatic leverage” in a statement earlier this month, saying those individuals had been “arbitrarily detained”.
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During his call with Mr Rouhani, Mr Johnson also raised Iran’s breaches of its nuclear deal with world powers, known as the Joint Comprehensive Plan of Action (JCPOA).
The Downing Street spokesperson said the PM “stressed that while the UK remains committed to making the Iran nuclear deal a success, Iran must stop all its nuclear activity that breaches the terms of the JCPOA and come back into compliance”.
“He stressed the importance of Iran seizing the opportunity presented by the United States’ willingness to return to the deal if Iran comes back into compliance,” they added.
“The prime minister underlined the need for Iran to cease wider destabilising activity and be a positive force in the Gulf region.”
Additional reporting by Press Association
