WASHINGTON - The United States said on Tuesday it was sending additional troops to the Middle East, after hundreds protesters stormed its embassy compound in Iraq, setting fires and chanting: "Death to America!"

Angered by US air raids that killed two dozen militia fighters on Sunday, supporters of the powerful Hashd al-Shaabi (Popular Mobilization Forces) paramilitary group spilled through checkpoints in the high-security Green Zone on Tuesday, demanding the removal of American troops from Iraq.

Reacting to the attack, US President Donald Trump said he held Tehran "fully responsible" for the incident, and said the protesters "will be held fully responsible", he wrote on Twitter on Tuesday.

"In addition, we expect Iraq to use its forces to protect the Embassy, and so notified!"

Trump later warned in a separate statement that Tehran would "pay a very big price" after the attack, but when asked later in the day about the possibility of tensions spiralling into a war with Iran, Trump told reporters: "Do I want to? No. I want to have peace. I like peace. And Iran should want to have peace more than anybody. So I don't see that happening."

US Secretary of State Mike Pompeo said the attack was "orchestrated by terrorists", one of whom he named as Abu Mahdi al-Muhandis.(FA)