A Namazi family statement posted online described the sentences as "beyond comprehension".
Iran has sentenced Siamak Namazi, a U.S.
UNICEF voiced its "deep sadness and personal concern" over the sentence, appealing for his release on humanitarian grounds.
Unicef issued a statement last month saying it was "deeply concerned about his health and well-being".
Iranian officials privately say that their country has an obligation to secure the release of its nationals who have been jailed overseas for helping Tehran bypass sanctions - in some cases to obtain humanitarian supplies and medicine.
The Mizan report said Nizar Zakka, a US permanent resident from Lebanon, also received a 10-year prison sentence. Siamak Namazi and his father, Baquer Namazi, were jailed for "collaborating with the hostile American government", the Mizan news agency reported on October 18. They were identified on social media as Farhad Abd-Saleh and Alireza Omidvar. It was unclear if they had lawyers or if they were among the two previously mentioned by Mizan.
The family lived outside NY for a period after the Islamic Revolution that toppled the USA -backed shah in 1979, though later returned to Iran, she said.
Parsi said Siamak Namazi's prominence also made him a target for hardliners on both sides: a 2015 article in the Daily Beast, published shortly before his arrest, portrayed him as lobbying overseas for Iranian interests. In May 2015, a hard-line Iranian website called Fardanews specifically pointed to him in a highly critical article, accusing him of being part of efforts to allow the West to infiltrate Iran. The web site said the video depicted "the first images of the moment of Siamak Namazi's arrest".
Watch Donald Trump's apology for comments made in 2005 video
After originally downplaying his remarks as "locker-room banter", Trump issued another statement apologizing for his remarks. Portman, a Terrace Park Republican, said he continues to believe "our country can not afford a Hillary Clinton presidency".
The short video opens with pictures of previously captured American drones and U.S. sailors in Iran.
The minute-long video showed Siamak Namazi, his USA passport, an ID card and a clip of him in a conference room with his arms raised, all set to music, according to The Associated Press.
Since Iran does not recognize dual nationalities, those detained can not receive consular assistance. More recently he ran Hamyaran, an umbrella agency for Iranian non-governmental organisations.
It was presented with dramatic music alongside images of his United States passport and shots of Washington Post journalist Jason Rezaian who spent two years in prison on espionage charges.
Almost a month after a prisoner deal between Washington and Tehran, the friends and family of business consultant Siamak Namazi - who holds degrees from Tufts and Rutgers universities and has ties to many Washington foreign policy insiders - fear he has been forgotten in the warm afterglow of last month's swap and are pressing the Obama administration to step up efforts to free him.
Security officials have arrested dozens of artists, journalists and businessmen, including Iranians holding joint American, European or Canadian citizenship, as part of a crackdown on "Western infiltration".
In its statement, the State Department also raised the case of Robert Levinson, a former Federal Bureau of Investigation agent and ex-CIA contractor who went missing on Iran s Kish Island in 2007.
"As President (Barack) Obama stated last January, we will not rest until the Levinson family is whole again".
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