One of Iran's highest ranking military officers has been killed in a US airstrike at Baghdad International Airport on Thursday (local time).

Iraqi officials said Major General Qassem Soleimani, head of Iran's elite Quds Force, was killed in the attack, which was blamed on the United States.

The Pentagon has confirmed the US is responsible for the attack and says it was ordered by Donald Trump himself.

"At the direction of the President, the US military has taken decisive defensive action to protect US personnel abroad by killing Qasem Soleimani," the Pentagon said in a statement.

"This strike was aimed at deterring future Iranian attack plans. The United States will continue to take all necessary action to protect our people and our interests wherever they are around the world."

The airstrike comes after the US embassy compound in Baghdad was attacked on New Year's Eve (local time) and is being labelled by The Guardian as "a dramatic escalation of an already bloody struggle between Washington and Tehran for influence across the region".

Abu Mahdi al-Muhandis, the deputy commander of Iran-backed militias known as the Popular Mobilization Forces (PMF), was also killed in the airstrike, Iraqi officials said. 

A PMF official said seven people were killed in the attack on the Baghdad International Airport.

Iranian state TV is said to be mourning the death of Soleimani.

Tension between the US and Iran spiked after an American contractor was killed in Iraq on December 27. US officials blamed Iranian-backed militia Kata'ib Hezbollah for the attack and subsequently carried out military strikes against the militia, which killed at least 25 of its fighters.

That attack was condemned by Iraq, Russia and Syria, but celebrated by Israel.

It also triggered protests in the streets of Iraq, including the attack on the US embassy in Baghdad reportedly by Iranian-backed militia.

The to-and-fro has come at a time of particular unrest in Iraq, with thousands of protesters demonstrating against the government and militias such as Kata'ib Hezbollah. More than 450 people have died so far in unrest related to the protests.

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Earlier this week, 700 US paratroopers were sent to Kuwait from their base in North Carolina. Esper said the troops were "defensive support" to be deployed if trouble in the region continued, reports AP.

Relations between the US and Iran - already strained - further soured after Donald Trump pulled out of a nuclear deal with Tehran last year and reimposed harsh sanctions on the country.

Many are pointing to the death of Soleimani as a turning point in the region, with BBC correspondent Nafiseh Kohnavard writing on Twitter it was "beginning of the end".

Soleimani became head of the Quds Force in 1998 and played a key role in fighting in Syria and Iraq, according to Reuters.