Iran has said the United States showed its "support for terrorism" by carrying out air attacks on the Shia armed group Kataib Hezbollah in Iraq and Syria.

The Pentagon said on Sunday that it had targeted the Iran-linked militia group in western Iraq and eastern Syria in response to the killing of a US civilian contractor two days earlier.

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Iraqi security and militia sources said at least 25 fighters had been killed and 55 others wounded in the air attacks in Iraq which the US described as "defensive strikes".

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At least four Kataib Hezbollah commanders were among the dead, the sources said, adding that one of the raids had hit the Iran-backed group's headquarters near the western al-Qaim district on the border with Syria.

"These attacks have once again proved America's false claims in fighting Daesh... as the United States has targeted the positions of forces that over the years have inflicted heavy blows to Daesh terrorists," Iran's government spokesman Abbas Mousavi said, referring to ISIL (ISIS).

"With these attacks, America has shown its firm support for terrorism and its neglect for the independence and sovereignty of countries and it must accept consequences for its illegal act," he said in a statement.

The spokesman said the presence of foreign forces in the region was the cause of insecurity and tensions. "America must put an end to its occupying presence," said Mousavi.

US-Iran tensions have soared since Washington pulled out of a landmark nuclear agreement with Tehran last year and began reimposing crippling sanctions.

'Violation of Iraqi sovereignty'

Meanwhile, Iraq also condemned the US attack against the Kataib Hezbollah armed group's positions as a "violation of Iraqi sovereignty".

In a statement on Sunday, Iraqi Prime Minister Adel Abdul Mahdi called the move a "dangerous escalation that threatens the security of Iraq and the region".

Abdul Mahdi said US Secretary of Defense Mark Esper had called him about half an hour before the US raids to tell him of the US intentions to hit bases belonging to the armed group suspected of being behind Friday's rocket attack. He said he asked Esper to call off US retaliation plans.

The statement said Iraqi President Barham Salih, who also condemned the attack, had received advance notice from a US diplomat and asked unsuccessfully for the US to call it off.

Speaking from Baghdad, Al Jazeera's Simona Foltyn said the Iraqi government's response would try to balance between factions that are supportive of the US and others closer to Iran.

"The government itself is not a homogeneous entity... The response of the government will try to balance these two sides," she said.

Another powerful pro-Iran faction in Iraq, Asaib Ahl al-Haq - whose leaders were recently hit with US sanctions - called for the US to withdraw from the country.

"The American military presence has become a burden for the Iraqi state and a source of threat against our forces," it said in a statement. "It is therefore imperative for all of us to do everything to expel them by all legitimate means."

Lebanon's powerful Shia group Hezbollah, also backed by Iran, condemned the US for attacking groups that helped it defeat ISIL.

US claims retaliatory attack

The US air attacks followed a rocket attack on Friday that killed a US civilian contractor and injured four US service members, as well as two members of the Iraqi Security Forces near the oil-rich city of Kirkuk.

The US accused the group of the attack.

"In response to repeated Kataib Hizbollah (KH) attacks on Iraqi bases that host Operation Inherent Resolve [OIR] coalition forces, US forces have conducted precision defensive attacks against five KH facilities in Iraq and Syria that will degrade KH's ability to conduct future attacks against OIR coalition forces," chief Pentagon spokesman Jonathan Hoffman said in a statement.

The targets - three in Iraq and two in Syria - included weapons storage facilities and command locations used to plan and execute attacks, the statement added.

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Following the move, US Secretary of State Mike Pompeo said top officials had briefed President Donald Trump on the attacks.

"We will not stand for the Islamic Republic of Iran to take actions that put American men and women in jeopardy," Pompeo told reporters after the briefing, which took place at Trump's Mar-a-Lago club in Palm Beach, Florida.

Esper described the attacks as successful, and said the US could take "additional action".

Earlier this month, Pompeo blamed Iranian-backed forces for the attacks and warned Iran that any attacks by Tehran or proxies that harmed Americans or allies would be "answered with a decisive US response".

Continuing protests in Iraq

The escalations come as Iraq is gripped by its biggest anti-government street protests since the US-led invasion of 2003 that toppled dictator Saddam Hussein.

Protesters, many of whom grew up in the post-Saddam era, have vented their anger at a government they consider inept, corrupt and beholden to Iran.

About 460 people have died in protest-related violence and some 25,000 have been wounded, but rallies and sit-ins have continued.

Since October 28, at least 11 attacks have hit Iraqi military bases where US soldiers or diplomats are deployed, including five rockets that hit Ain al-Asad airbase on December 3, just four days after US Vice President Mike Pence visited troops there.