The U.S. military says it is checking the reports by Iraqi security force officials.
Ammar Hakim's father heads the Supreme Council for the Islamic Revolution in Iraq (SCIRI), the biggest party in Shi'ite Iraqi Prime Minister Nuri al-Maliki's national-unity cabinet.
It was not immediately clear why he was reportedly detained.
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SUNNI, SHI'A: Iraq is riven along sectarian lines, faults that frequently produce violent clashes and are a constant source of tension. Sectarian concerns drive much of Iraqi politics and are the main threat to the country's fragile security environment.