The raid was the most brazen action by Iraqi forces against a major Iran-backed militia group in years and targeted the Kataib Hezbollah faction.
Mustafa al Kazimi will have to pick a side if he wants to enact meaningful change.
An Iraqi official said the rocket had struck near the US Embassy in the Green Zone where government buildings and foreign embassies are located.
The US strikes that target Shia militias actually target a branch of the Iraqi Army.
The US strike on Baghdad's international airport early Friday also killed the PMU leader's personal friend and top commander in Iran's Revolutionary Guard Corps, Qasem Soleimani.
The US killed the militia's commander Abu Mahdi al Muhandis along with the most influential Iranian commander Qasem Solaimani following militia's siege of the US consulate in Baghdad.
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