The husband of Nazanin Zaghari-Ratcliffe had "good" talks with Liz Truss, ahead of her meeting with the Iranian foreign minister to call for the immediate release of detained UK nationals.
Richard Ratcliffe told the foreign secretary during a 10-minute phone call on Sunday that his wife’s case should be the top priority and he wanted to see the government tackle hostage-taking head on.
Ms Truss later said she will push for UK nationals trapped in Iran to be released, during a meeting with Hossein Amir-Abdollahian at the UN General Assembly in New York on Monday.
She is expected to bring up the cases of Ms Zaghari-Ratcliffe, Anoosheh Ashoori and Morad Tahbaz.
Ms Truss said: "I will be asking Iran to ensure the immediate and permanent release of all arbitrarily detained British nationals in Iran, and to begin working with us to mend our fractured relations."
She had earlier spoken to Mr Ratcliffe while at the airport before leaving for New York, and is said to have shared his concerns about the situation.
Mr Ratcliffe’s wife, a British-Iranian dual national, has been in custody in Iran since 2016 after being accused of plotting to overthrow the government.
Mr Ratcliffe told the PA news agency: "It was nice to hear, considering she is three days into the new job, and is earlier than expected.
"I think it went well overall, she asked me how I wanted to see things – I told her that Nazanin has been used as a bargaining chip of the Iranian government for some time and that I wanted to see Iranian hostage-taking disincentivised."
Mr Ratcliffe earlier said that he had given Ms Truss the names of 10 people he accuses of being involved with "hostage-taking" in Iran.
He called on the foreign secretary to ensure Iran is made aware this is an "unacceptable practice".
Foreign Office minister James Cleverly told Sky News the release of dual nationals by Iran will be "top of the agenda" when Ms Truss meets her Iranian counterpart.
"We will continue pushing and we will not rest until we get them all home," he told Kay Burley.
"Their incarceration is arbitrary, it’s completely unjustified and we have made it clear that we will not stop working to get those British dual nationals home."
Richard Ratcliffe is due to appear on Sky News this morning at around 7.35am.