A volley of rockets on Monday targeted the high-security Green Zone in the Iraqi capital, where the American and other foreign embassies are based.

The attack was the third in a week to target Western diplomatic, military or commercial installations across Iraq after four months of relative calm.

Iran's Foreign Minister Mohammad Javad Zarif said,

"We underline the need for the Iraqi government to identify the perpetrators of these incidents," Iran's Foreign Minister Mohammad Javad Zarif said after talks in Tehran with his Iraqi counterpart Fuad Hussein.

"Recent attacks and incidents... could be designed to disrupt Iranian-Iraqi relations and destabilise" Baghdad, Zarif said in a statement.

The meeting comes after Washington retaliated for the attacks by launching overnight Thursday an air strike on facilities in eastern Syria used by Iran-backed militias near the border with Iraq.

The Pentagon confirmed President Joe Biden had authorised the strikes "in response to recent attacks against American and coalition personnel in Iraq".

Secretary of State Antony Blinken said Friday the administration wanted to make it "very, very clear -- notably to Iran-- that they cannot act with impunity against our people, our partners, our interests."

The rocket attacks in Baghdad have not been claimed, but Washington said intelligence showed hardline pro-Iran factions operating under the umbrella of Iraq's state-sponsored Hashed al-Shaabi paramilitary force were responsible.

Zarif "condemned the dangerous action of the United States in attacking Iraqi forces in the border area" between Iraq and Syria, saying the air strikes were "illegal" and in "violation of the sovereignty" of both countries, according to the statement.

Iraq, scarred by decades of war and insurgency, has been a strategic battleground for arch-foes the United States and Iran, both allies of Baghdad who remain sharply at odds over Iran's nuclear programme.

The US strike was its first military action targeting such groups since Biden took office five weeks ago and came amid heightened tensions over Iran's nuclear programme after the president opened the door to resuming negotiations with Tehran toward salvaging a 2015 nuclear deal.