The measure from the US Treasury Department targets both Sohrab Soleimani and the Tehran Prisons Organization.
Soleimani is the younger brother of Major General Qassem Soleimani, who runs the foreign operations arm of Iran's Revolutionary Guards and who has been photographed visiting Iranian-led fighting forces in Syria and Iraq. Qassem Soleimani is already subject to US sanctions.
Sohrab Soleimani is the supervisor of the Office of the Deputy for Security and Law Enforcement of the State Prisons Organisation, according to a US Treasury statement. He used to be the director general of the Tehran Prisons Organization
A US-Iranian man and his wife were formally charged last month with holding social gatherings deemed illicit under Iran's Islamic laws.
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"The sanctions against human rights abusers in Iran's prison come at a time when Iran continues to unjustly detain in its prisons various foreigners including US citizens," White House Press Secretary Sean Spicer said a news briefing.
"We join recent calls by international organizations and UN human rights experts for the immediate release of all US citizens unjustly detained or missing in Iran."
The statement cited one April 2014 event at Evin Prison in which it said prison officials attacked and beat political prisoners, leaving more than 30 injured, with some denied medical treatment and held in solitary confinement afterwards.
The Treasury today also imposed counterterrorism sanctions on two Libyans, identified as Ali Admidah al-Safrani and Abd al Hadi Zarqun, and an Algerian, Hamma Hamani, accused of ties to the Islamic State group.
Two Canadians currently in Syria, Tarek Sakr and Farah Mohamed Shirdon, were also addded to the sanctions list.
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