BAGHDAD—An attempt by supporters of Iran-backed militias to storm the U.S. Embassy here went into retreat Wednesday, as protesters withdrew from the area after their leadership ordered the suspension of a violent challenge to American troop presence in Iraq.

The retreat was instigated by the Popular Mobilization Forces, an umbrella body for dozens of militia groups including factions aligned with Iran. The PMF said protesters demanding the expulsion of American troops from Iraq had delivered their message to the U.S.

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