He said if the court accepts the reasoning "there will remain no conviction that would justify such a heavy punishment."
Iranian prosecutors said Hekmati received special training and served at U.S. military bases in Iraq and Afghanistan before heading to Iran as a spy.
The Obama administration in November asked for Iran to free Hekmati and two other Americans believed held there, as relations recently have thawed between Washington and Rouhani. The call comes as world powers continue negotiations with Iran over its contested nuclear program.
Hekmati's family, which lives in the Flint, Michigan, area, says he is innocent and only went to Iran to visit his grandmothers. The U.S. government repeatedly has denied the 31 year old is a spy. The Associated Press left phone and email messages for family representatives Sunday.
Previously, Tabatabaei said he sought Hekmati's conditional freedom from Evin prison, north of the capital, Tehran. Hekmati has been behind bars since his arrest.
Conditional freedom could allow Hekmati to leave the country, depending on what a court decides. That could allow Hekmati to visit his father Ali Hekmati, a professor at Mott Community College in Flint, Michigan, who family members say has been diagnosed with terminal brain cancer and recently suffered a stroke.
Tabatabaei said Hekmati's situation is fine in prison and "He spends most of his time reading."
Associated Press reporter David N. Goodman in Detroit contributed to this story.