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Fallujah, a former insurgent stronghold, is located 65 kilometers (40 miles) west of Baghdad.
The case of al-Issawi will likely fuel the simmering political infighting over power sharing in post-Saddam Iraq.
On Friday, Sunni Deputy Prime Minister Saleh al-Mutlaq threatened that his Iraqiya bloc could withdraw from the political process altogether if lawmakers and independent bodies are not allowed to monitor the investigation involving al-Issawi's staff.
The arrests came a year after the government arrested nearly 70 bodyguards assigned to Sunni Vice President Tariq al-Hashemi on terrorism-related charges. Then al-Hashemi himself was convicted of orchestrating death squads, a charge he dismissed as politically motivated.
Iraqi courts have since handed down multiple death sentences against him. He now lives in neighboring Turkey.
Associated Press writer Sinan Salaheddin in Baghdad contributed.