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US forces targeted facilities used by Iran-backed militants in Iraq in response to attacks on American personnel in both that country and Syria, Defense Secretary Lloyd Austin said on Tuesday.

The strikes - which will add to already significant pressure for US forces to depart the country - came just days after American troops in western Iraq were targeted with ballistic missiles and rockets, an attack the Pentagon blamed on militants supported by Tehran.

"US military forces conducted necessary and proportionate strikes on three facilities used by the Iranian-backed Ketaeb Hezbollah militia group and other Iran-affiliated groups in Iraq," Austin said in a statement.

"These precision strikes are in direct response to a series of escalatory attacks against US and coalition personnel in Iraq and Syria by Iranian-sponsored militias," he said, referring to the US-led international coalition against the Islamic State (IS) jihadist group.

"We do not seek to escalate the conflict in the region," but "are fully prepared to take further measures to protect our people and our facilities," Austin added.

US Central Command said the strikes targeted Ketaeb Hezbollah "headquarters, storage, and training locations for rocket, missile, and one-way attack UAV (drone) capabilities."

US and allied forces in Iraq and Syria have been targeted in more than 150 attacks since mid-October, according to the Pentagon, and Washington has carried out retaliatory strikes in both countries, including one that killed a pro-Iran commander in Baghdad earlier this month.

That strike in particular infuriated the Iraqi government, and Prime Minister Mohammed Shia al-Sudani has called for the US-led coalition against IS jihadists to depart the country.

The United States has around 2,500 troops in Iraq and 900 in Syria as part of efforts to prevent a resurgence of IS, which once held significant territory in both countries.