WASHINGTON (AP) — The U.S. has carried out military strikes in Iraq and Syria targeting a militia blamed for a rocket attack that killed an American contractor, a Defense Department spokesman said Sunday.

U.S. forces conducted “precision defensive strikes” against five sites of Kataeb Hezbollah, or Hezbollah Brigades, an Iran-backed Iraqi militia, spokesman Jonathan Hoffman said in a statement.

The U.S. blames the militia for a rocket barrage Friday that killed a U.S. defense contractor at a military compound near Kirkuk, in northern Iraq. Officials said attackers fired as many as 30 rockets in Friday's assault.

The Defense Department said the U.S. hit three of the militia's sites in Iraq and two in Syria, including weapon depots and the militia's command and control bases.

The strikes were carried out by U.S. Air Force F-15 Strike Eagles, said a U.S. official who was not authorized to publicly discuss details of the attacks. At the ammunition storage facilities that were struck, significant secondary explosions were observed.

Hoffman said the U.S. attacks would limit the militia's ability to carry out future strikes against Americans and their Iraqi allies.

Iraq’s Joint Operations Command said in a statement that three U.S. airstrikes on Sunday evening Iraq time hit the headquarters of the Hezbollah Brigades at the Iraq-Syria border, killing four fighters.

Iraq’s Hezbollah Brigades, a separate force from the Lebanese group Hezbollah, operate under the umbrella of the state-sanctioned militias known collectively as the Popular Mobilization Forces. Many of them are supported by Iran.

The Popular Mobilization Forces said Sunday that the U.S. strikes killed at least 19 of Kataeb Hezbollah's members.

Kataeb Hezbollah is led by Abu Mahdi al-Muhandis, one of Iraq’s most powerful men. He once battled U.S. troops and is now the deputy head of the Popular Mobilization Forces.

In 2009, the State Department linked him to the elite Quds Force of Iran’s Revolutionary Guard, designated a foreign terrorist organization by President Donald Trump earlier this year.

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The U.S. maintains some 5,000 troops in Iraq. They are there based on an invitation by the Iraqi government to assist and train in the fight against the Islamic State group.

The militia strike and U.S. counter-strike come as months of political turmoil roil Iraq. About 500 people have died in anti-government protests in recent months, most of them demonstrators killed by Iraqi security forces.

The mass uprisings prompted the resignation of Prime Minister Adel Abdul-Mahdi late last month. Abdul-Mahdi remains for now in a caretaker capacity.

Abdul-Mahdi had made no public comment on Friday’s militia attack but condemned the U.S. retaliatory strike on Sunday. He called it a violation of Iraqi sovereignty and a “dangerous escalation that threatens the security of Iraq and the region.”

In a statement, Abdul-Mahdi said Defense Secretary Mark Esper had called him about a half-hour before the U.S. strikes to tell him of U.S. intentions to hit bases of the militia suspected of being behind Friday's rocket attack. Abdul-Mahdi said in the statement he asked Esper to call off U.S. retaliation plans.

The statement said Iraqi President Barham Salih also received advance notice from a U.S. diplomat, and also asked unsuccessfully for Americans to call off it off.

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Associated Press writer Zeina Karam contributed from Beirut.

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This story has been corrected to show that about 500 people have died in recent anti-government protests, not nearly 600.