Javad Zarif said he was offering to free the British-Iranian mother, who has been jailed in the country for three years, in exchange for an Iranian woman held in Australia.
And he claimed that Iran had told Donald Trump's White House team six months ago that his country was open to a prisoner swap scheme but had not received a response.
“We have an Iranian lady in Australia who gave birth to a child in prison, not even on bail, inside prison, on an extradition request by the United States because she was responsible as a translator in a, whatever, in a purchase operation – purchase – of some transmission equipment for Iranian broadcasting company,” he said.
“That’s her charge. She has been lingering in an Australian jail for the past three years.
“Now we hear about Nazanin Zaghari [Ratcliffe] and her child, and I feel sorry for them, and I have done my best to help, but nobody talks about this lady in Australia who gave birth to a child in prison whose child is growing up outside prison with mother in prison.
“So, what can I do as a foreign minister? And I put this offer on the table publicly now. Exchange them.”
Ms Zaghari-Ratcliffe was arrested at Tehran’s Imam Khomeini airport on 3 April, 2016, when trying to return to London after a holiday with her then 21-month-old daughter, Gabriella.
She was later held in solitary confinement for eight months, before being handed a five-year jail sentence on espionage charges, which she denies.
Speaking at the Asia Society, Mr Zarif went on: “All these people that are in prison, inside the United States, on extradition request from the United States – we believe their charges are phoney.
“The United States believes the charges against these people in Iran are phoney. Fine. Let’s not discuss that. Let’s have an exchange.
“I’m ready to do it. And I have authority to do it.
“We’ve informed the government of the United States six months ago that we are ready – not a response yet. If they tell you anything else, they’re lying.”
Mr Zarif may have been referring to Negar Ghodsi-Kani, an Iranian who was arrested in June 2017 while pregnant for allegedly violating US commercial laws in Australia. Iranian officials have repeatedly raised her case as a “violation” of human rights.
Ms Zaghari-Ratcliffe, 40, staged a hunger strike about the alleged refusal to grant her medical treatment in jail.
Her husband, Richard Ratcliffe, said his wife’s treatment at the hands of her captors had amounted to torture.
Hadi Ghaemi, executive director of IranHumanRights.org, said the country should free all dual nationals imprisoned on “trumped-up” charges.