The United States has launched a series of air raids in Iraq against several locations of an Iran-backed militia that it blamed for an earlier rocket attack that killed and wounded US and British troops.

Among the facilities attacked late on Thursday was an airport under construction in the holy city of Karbala, an Iraqi airport official confirmed.

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Iraq's military said in a statement that the US air raids killed one civilian and five security personnel.

In a statement, the Pentagon said the US conducted "defensive precision strikes" against Kataib Hezbollah facilities across Iraq.

"These weapons-storage facilities include facilities that housed weapons used to target US and coalition troops," it said.

Separately, UK Foreign Secretary Dominic Raab described the air raids as a "proportionate" response to the rocket attack south of the capital, Baghdad, that killed two US troops and a British soldier.

"UK forces are in Iraq with coalition partners to help the country counter terrorist activity and anyone seeking to harm them can expect a strong response," Raab said in a statement.

Al Jazeera's Simona Foltyn, reporting from Baghdad, said aside from Kataib Hezbollah, other militia groups under the Popular Mobilisation Forces (PMF, also known as PMU) were also hit south of Iraq's capital as well as in Babylon and Karbala.

A US official told The Associated Press news agency that the raids were a joint operation with the British. The officials spoke to AP on condition of anonymity.

Earlier on Thursday, US President Donald Trump gave the Pentagon the authority to respond after a rocket barrage killed two US troops and a British soldier, again raising tensions with Iran after the two countries came to the brink of war earlier this year.

Washington had blamed Kataib Hezbollah for a strike in December that killed a US contractor, leading to a cycle of tit-for-tat confrontations that culminated in the January 3 US assassination of top Iranian general Qassem Soleimani and a retaliatory Iranian missile attack that left more than 100 US troops with brain injuries.

In the latest rocket attack, responsibility for which has not been claimed, some 14 US-led coalition personnel were also wounded, including US, British, Polish and others. Private industry contractors were among the wounded.

Following the retaliatory attack, Iran warned Trump against taking "dangerous actions".

"Instead of dangerous actions and baseless accusations, Mr Trump should reconsider the presence and behaviour of his troops in the area," foreign ministry spokesman Abbas Mousavi said in a statement.

Al Jazeera's Foltyn said it remains to be seen how the militia groups will respond to the retaliatory strikes, but added that the latest attacks are likely to once again ignite calls in Iraq for the expulsion of US troops.

She noted that the Popular Mobilisation Forces commanders have already come out to condemn the latest raids "as a violation of Iraq's sovereignty".

Kataib Hezbollah was one of the Iraqi militia groups that helped defeat the ISIL (ISIS) group.