Baghdad: The Pentagon says the US military has killed Major-General Qassem Soleimani, head of Iran's elite Quds Force, at the direction of US President Donald Trump.

"This strike was aimed at deterring future Iranian attack plans," the Pentagon said in a statement.

The key Iranian military leader and an Iraqi militia commander, Abu Mahdi al-Muhandis, were assassinated in an air strike on their convoy in Baghdad airport, an Iraqi militia spokesman told Reuters.

Revolutionary Guard's foreign wing, or Quds Force, General Qassem Soleimani, centre. Credit:AP

"The American and Israeli enemy is responsible for killing the mujahideen Abu Mahdi al-Muhandis and Qassem Soleimani," said Ahmed al-Assadi, a spokesman for Iraq's Popular Mobilisation Forces umbrella grouping of Iran-backed militias.