Iraq's government condemned overnight U.S. airstrikes south of Baghdad that killed eight members of Iran-aligned Iraqi armed group Kataib Hezbollah, saying they were a "dangerous escalation" not coordinated with authorities.

The U.S. has carried out two series of strikes in Iraq since Tuesday, in response to more than 60 attacks by Iran-aligned militias against forces in the region, and destroyed a Kataib Hezbollah operations centre and a command and control node.

Until this week, the United States had been reluctant to retaliate in Iraq because of the delicate political situation in Baghdad, where they have sought closer cooperation, and in an effort to avoid regional spillover from the Gaza war.

The U.S. had previously undertaken three separate sets of strikes in Syria in response to the attacks, which began on Oct. 17 and have been linked by Iraqi militia groups to U.S. support for Israel in its bombardment of Gaza following attacks by Palestinian militant group Hamas on Israel.

Kataib Hezbollah said the strikes in Iraq killed eight of its members in its stronghold of Jurf al-Sakhar, south of Baghdad.

In a statement, it threatened to attack a wider array of targets if U.S. strikes continued.

The Iraqi government condemned the U.S. strikes as "a clear violation of sovereignty and an attempt to disrupt the stable internal security situation," while also noting attacks by armed groups went against Iraq's national interest.

It said in a statement that the strikes were a violation of the advisory role of international forces in Iraq to fight the remnants of the Islamic State militant group - a coalition that a number of factions in Iraq's Shi'ite Muslim ruling coalition say they want ousted.

About 24 hours earlier, U.S. forces were attacked by close-range ballistic missiles at Ain al-Asad airbase west of Baghdad, resulting in eight injuries and minor infrastructure damage, U.S. officials said.

A U.S. military AC-130 aircraft responded in self-defence, killing Iranian-backed militants, the U.S. officials said.

Kataib Hezbollah said one their members was killed in that strike.

The group is part of Iraq's Popular Mobilisation Forces (PMF), a group of many mainly Shi'ite Muslim armed groups that was formed in 2014 to fight Islamic State and subsequently recognised as an official security agency by Iraq's government.

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.