The husband of Nazanin Zaghari-Ratcliffe, the British-Iranian woman detained in Iran since 2016 on spying charges, has accused the authorities in Tehran of “playing games” with his family’s hopes, as he called on the Foreign Office to escalate its attempts to secure her release by the summer.

Richard Ratcliffe said he was still hopeful his wife would soon be released on health grounds, after she was finally allowed to have tests and MRI scans to determine whether the lumps in her breasts are cancerous. But speaking a day after the Iranian foreign minister, Mohammad Javad Zarif, appeared to retract an offer of a prisoner swap, Ratcliffe spoke angrily of the authorities who have separated his wife from him and their four-year-old daughter, Gabriella.

“Iran is holding people prisoner and using them as diplomatic leverage,” he said. “The situation is not helped by countries pretending it’s not happening. It requires coordinated work, a joint statement from the UK and other like-minded countries, saying they are going to stand against arbitrary detention of foreign citizens.”

Facebook Twitter Pinterest Richard Ratcliffe delivers a Mother’s Day card outside the Iranian embassy in March. Photograph: Will Oliver/EPA

Ratcliffe worries that if progress is not made by his wife’s birthday in mid-June, she may go on another hunger strike. “Either we get good news soon, or another bump of bad news. I’m not sure from the way the Iranian foreign minister used Nazanin this week that the Iranian authorities quite appreciate that timescale. If they did, I don’t think they’d be game-playing in that way.”

The deadline of mid-June is also significant because Ratcliffe would like to bring Gabriella – who has been living with her grandparents in Tehran since her mother’s arrest three years ago – back to England over the summer, to start school near his home in West Hampstead in September.

Zarif said in a speech in New York last Wednesday he had the power to authorise the release of Zaghari-Ratcliffe – who was granted diplomatic protection by the UK in March – in return for freeing an Iranian prisoner held in Australia. But the following day he said she could not be included in any prisoner swaps.

Ratcliffe said: “If you want a prisoner swap, the last place you would negotiate it is on television, which is what they did.” He added that Iran knows the UK’s official policy is not to engage in prisoner swaps.

“Off stage, we had been seeing progress towards a medical release,” he said. “I still cling to hope.”