Majid Kazemi was sentenced to death on January 9 after the regime accused him of being involved in deaths of three government militia members during a protest rally.
The protest is one of many in Tehran since 22-year-old student Mahsa Amini died in custody in September after being detained by the state's morality police for allegedly violating Iran's strict dress code for women.
Asked on Tuesday if Australia had a responsibility to intervene, Treasurer Jim Chalmers told ABC TV he didn't have an update on the case.
But he said what was happening in Iran, where multiple people have recently been sentenced to death in the wake of the protests, was "troubling".
"We'll do what we often do when it comes to these sorts of cases, which is explore our options and work through them in a considered way," he said.
"If we've got an update to provide then we'll do that through a relevant minister."
Iranian Australians are angry about what happened to Ms Amini and have been holding regular weekend rallies decrying her fate and criticising the Iranian regime.
Last week, Australian Greens senator Jordon Steele-John wrote to the Iranian ambassador stating his "political sponsorship" of Mr Kazemi.
"Every day we wake up to the news that more Iranian freedom protesters have been sentenced to death. This must end," he said.
His Greens colleague Sarah Hanson-Young has offered to act as a political sponsor for arrested Iranian actress Katayoun Riahi, who was detained after supporting protesters.
"The trials and sentences have not been free from bias in cases against protesters," she wrote in a letter to Iran's ambassador in Canberra.
Senator Hanson-Young said she would politically sponsor Mrs Riahi, adding the recently released actress was under enormous pressure to denounce her support for the protesters.
She also requested an update of Mrs Riahi's welfare and case after she was reportedly violently restrained before her court session and taken to hospital in an ambulance.
"Mrs Riahi has been a voice for Iranian women and girls," she wrote.
"I extend solidarity to Katayoun Riahi who is demanding an end to violence and oppression in Iran."
Opposition foreign affairs spokesman Simon Birmingham offered bipartisan support to any actions taken by the government.
He said options included further sanctions, listing Iran's revolutionary guard as a terrorist organisation and expelling Iranian diplomats from Australia.
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