"Iran will be held fully responsible for lives lost, or damage incurred, at any of our facilities," Trump said on Twitter, after pro-Iranian protestors stormed the US embassy in Baghdad.

"They will pay a very BIG PRICE! This is not a Warning, it is a Threat," wrote Trump, adding "Happy New Year!"

Trump meanwhile thanked Iraqi Prime Minister Adel Abdel Mahdi and President Barham Saleh for "their rapid response upon request" to the embassy attack.

Trump spoke with Abdel Mahdi earlier by telephone, stressing the need to protect Americans and US facilities in Iraq, the White House said.