Iran has flatly rejected US accusations that it is behind violent protests which broke out at the American embassy in Baghdad in response to US airstrikes on militia groups in Iraq.

In a tweet on Tuesday, US President Donald Trump accused Iran of "orchestrating an attack on the US Embassy in Iraq," and said Tehran will be held "fully responsible.” Trump also called on "millions" of Iraqis to resist Iran.

Iran hit back at the “audacity” of Washington to blame Tehran for the attacks in a statement posted by the Foreign Ministry.

"America has the surprising audacity of attributing to Iran the protests of the Iraqi people against (Washington's) savage killing of at least 25 Iraqis…," it said.

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The US hit five Kataib Hezbollah targets in Iraq and Syria last week in retaliation for an attack on a US coalition base near Kirkuk, which no group took responsibility for, but which Washington blamed on the Iranian-backed militia.

Iraqi Prime Minister Adel Abdul Mahdi condemned the airstrikes, calling them a violation of Iraq's sovereignty and said there could be "grave consequences." Protesters then stormed the US embassy compound on Tuesday, shouting "death to America” and waving Hezbollah flags.

Washington announced earlier Tuesday that it was sending reinforcements to the Baghdad embassy, in what Defense Secretary Mark Esper said were measures “to ensure our right of self-defense.”

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