According to the outlet, the same judge who ruled on the order had also dealt last month with the case of two Iraqis arrested in 2008 in Basra on suspicions of posing a security threat and transferred to the US military.
The two men claimed they had been beaten, deprived of sleep and sexually abused while in US custody, the media said.
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The court ordered the ministry to search for reports containing any allegations of US military's mistreatment of Iraqis between 2004 and 2008 and to disclose the findings by November 26, the newspaper added.
The United States launched a military operation in Iraq in March 2003 to overthrow former Iraqi leader Saddam Hussein whom Washington accused of links to Al-Qaeda, the terrorist organization (banned in Russia) behind the 9/11 attacks.