The Hashed, a powerful paramilitary network integrated into Iraq's state security forces, ordered its backers to end their protest outside the US mission.

"You delivered your message," it said in a statement.

Thousands had massed outside the embassy in anger at deadly weekend US air strikes on pro-Iran Hashed faction, Kataeb Hezbollah.

Iraq's caretaker prime minister Adel Abdel Mahdi had called on the Hashed supporters to leave the embassy on Tuesday but most spent the night in dozens of tents pitched outside the perimeter wall.

On Wednesday, the Hashed called on supporters to regroup outside the high-security Green Zone where the mission is located.

An AFP photographer saw some protesters beginning to dismantle their tents.

But a leading Kataeb Hezbollah commander told AFP they would stay outside the embassy.

"We in Kataeb Hezbollah won't withdraw even if the others do," said the commander, who was among those outside.