The call was made in a letter to the head of Iran's judiciary.
Farahbakhsh's relatives say his trial took place some three weeks ago but they have not been informed about the court ruling.
"We visited him at the prison yesterday [March 12], and he wasn't feeling well again," Farahbakhsh's mother, Badri Farahbakhsh, told Radio Farda. "He has heart problems, he often feels pain in his [chest]. He hasn't committed any mistake or sin."
Farahbakhsh was arrested in November after he returned from a conference on economics in Thailand.
He has been reportedly charged with espionage.
Media and rights groups have expressed concern over his arrest and detention.
(with material from ILNA)