Cambridge-educated Kylie Moore-Gilbert, who was most recently a lecturer in Islamic Studies at Melbourne University, has been in Tehran's notorious Evin prison for more than a year, having reportedly been given a 10-year sentence.
"I beg you to act faster to end this terrible trauma that myself and my family must live through day after day" Dr Moore-Gilbert wrote in the June 2019 letter that was smuggled out of the prison and published by the Centre for Human Rights in Iran.
Dr Moore-Gilbert also wrote that she had travelled to Iran on a university program and had been doing research interviews.
"Unfortunately, one of my academic colleagues on this program and one of my interview subjects flagged me as suspicious to the Revolutionary Guards," she said.
She wrote again on Christmas Eve to say she had been kept in solitary confinement for extended periods, had been allowed only one three-minute phone call with her family in nine months and had undertaken five hunger strikes.
"I beg of you, Prime Minister Morrison, to take immediate action, as my physical and mental health continues to deteriorate with every additional day that I remain imprisoned in these conditions," she added.
When asked last month by reporters if he was concerned for Dr Moore-Gilbert's welfare, Mr Morrison said he was, adding: "As I am for any Australian who finds themselves in these types of situations."
Around the same time Iran's foreign ministry said it would not "give in to the political and smear campaigns" over the jailing.
The Australian government secured the release of dual British-Australian citizen Jolie King and her Australian boyfriend, Mark Firkin, in early October, some three months after they were arrested in Iran.
Other Britons imprisoned in Evin include Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori who are serving five and 10 year sentences respectively on charges disputed by the British Government.