Kurds control an autonomous region in north Iraq, and they also held the disputed Kirkuk province from 2003 until they were driven out last month by federal forces after Baghdad rejected an independence referendum.
Since then, hundreds of Iraqis have gathered at demonstrations in Kirkuk city, calling for human rights bodies to shed light on the whereabouts of relatives arrested by Kurdish forces.
"Two thousand people have been arrested since 2003," Khaled al-Mafarji, an Arab MP from Kirkuk, told AFP.
During the rally, relatives appealed directly for Abadi to intervene to help find their loved ones -- drawing a quick response from the Iraqi leader.
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"The prime minister has ordered investigations as demanded by the families of those arrested by Kurdish Asayesh members in Kirkuk province in order to know their fate," Abadi's office said later in a statement, referring to the Kurdish security services.
A senior Kurdish security official told AFP that any arrests were "measures taken to enforce the law".
One of those demonstrating yesterday, Najm al-Shahri, said Kurdish security forces arrested his son at home in 2007, when he was 17 years old.
Shahri said his son had been accused of "attacking US forces" who had intervened in Iraq three years earlier, leading to the downfall of dictator Saddam Hussein.
He said he wanted only one thing: "The body of my son or information about his fate".
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