Australia and the United States both condemned Iran's execution of Ruhullah Rawhani, a member of the minority religious group despised in Iran as a heretical offshoot of Islam.

The father of four was hanged for converting a Muslim to the Bahá'í religion.

However, Iran has denied the execution took place, angering Australian Bahá'ís and prompting an angry rebuttal from a Perth man claiming to be a relative of the dead man.

"They can't pretend he didn't exist," the man, identified only as Ruhi said in a statement released by the Australian Bahá'í community.

"They imprisoned him in September. They kept him in solitary confinement. They killed him. Relatives were called to the prison to collect his body and his burial was witnessed by them. So were the rope marks around his neck."

Australian Bahá'í Community spokeswoman Judy Hassall said she was alarmed by Iran's attempt to cover up the execution. "We have known of Mr Rawhani's imprisonment for months, as have governments around the world," she said.

"This attempt to hide the facts about Mr Rawhani's execution is just unbelievable."

AAP ss/lm