Namazi was detained as he arrived in Tehran in October 2015.
Siamak Namazi and his 80-year old father were convicted of "cooperating with the hostile American government" along with four other people including Nizar Zaka, a permanent USA resident from Lebanon who was arrested in November 2015.
An Iranian-American businessman and his 80-year-old father have been given 10 years in prison for espionage, Tehran's prosecutor said on Tuesday, prompting the U.S. to demand their release.
The Namazis are the latest of a string of dual nationals - including citizens from the United Kingdom and France - who have been imprisoned in what activists fear is a campaign to gather potential bargaining chips against western countries.
The detentions of Siamak and his father, Baquer Namazi, have drawn protests from the United States.
McCain said the video was just part of a pattern of intimidation against the U.S.by Iran, enabled by the Obama administration's pursuit of the Iran nuclear deal, which lifted sanctions on Iran in exchange for curbs to its nuclear program. On Tuesday, both he and his 80-year-old father, imprisoned in February, were sentenced to 10 years in prison for unspecified charges related to collaborating with hostile governments.
The widow of American boxing legend Muhammad Ali has called on Iran's supreme leader, Ali Khamenei, to free Iranian-Americans Siamak Namazi and his father Bagher Namazi.
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That deal also saw the US make a $400 million cash delivery to Iran.
It wasn't clear why hard-liners chose to release the video, which was posted online Monday by Iran's state-run Mizan judicial news agency.
Security officials have arrested dozens of artists, journalists and businessmen, including Iranians holding joint U.S., European, or Canadian citizenship, as part of a crackdown on "Western infiltration".
"My father has been handed practically a death sentence and it will be a criminal act by me, his only able son, not to fight for my father's life and freedom as well as that (of) my brother", wrote another son, Babak Namazi.
Baquer Namazi, a retired UNICEF representative in Somalia, Kenya, Egypt and other countries, and a former Iranian provincial governor, was described by a former United Nations colleague as having a "deep personal commitment to making life better for children and women". The motives behind these arrests have been lucidly explained, but news of detained Iranian Americans dies when there are no developments on the ground. He named them as Farhad Abdesaleh, Kamran Ghaderi and Alireza Omidvar, without elaborating.
According to a Huffington Post article written by a friend of the younger Namazi, Siamak was passionate about promoting better relations between the United States and Iran and wrote a study about how sanctions were blocking humanitarian trade.