Iraq's government on Tuesday condemned overnight U.S. air strikes on Iraqi military positions that it said killed one serviceman and wounded 18 people, calling them a "clear hostile act".

The United States carried out retaliatory air strikes on Monday in Iraq after a one-way drone attack earlier in the day by Iran-aligned militants that left one U.S. service member in critical condition and wounded two others.

The government condemned the U.S. strikes as "an unacceptable violation of Iraqi sovereignty" while stressing that attacks by armed groups against military bases hosting U.S-led coalition advisers are hostile acts and violate Iraqi sovereignty, a government statement said.

Two Iraqi security sources said overnight U.S. strikes targeted the headquarters of Iraqi armed group Kataib Hezbollah in the Iraqi city of Hilla south of Baghdad.

One fighter from Kataib Hezbollah was killed in the strikes and 16 were wounded, said two security sources on condition of anonymity.

The Iran-aligned Kataib Hezbollah criticised the government position for condemning the Iraqi militia attacks against the U.S.-led coalition targets, a security official from the group said in a social media post.

"...We warn those with weak souls, from the highest level to the lowest, not to test our patience," Abu Ali al-Askari said.

In a clear challenge to the government of Prime Minister Mohammed Shia al-Sudani, Askari vowed to continue attacks against U.S. forces.

Iraqi Prime Minister Mohammed Shia Al-Sudani has limited control over some Iran-backed factions, whose support he needed to win power a year ago and who now form a powerful bloc in his governing coalition. Many of the factions also do not see eye-to-eye on actions against U.S. forces.

The United States has 900 troops in Syria and 2,500 in Iraq on a mission it says aims to advise and assist local forces trying to prevent a resurgence of Islamic State, which in 2014 seized large swaths of both countries before being defeated.