Iraq has been pulled into the war sparked by US and Israeli strikes on Iran on February 28, and which has since engulfed much of the region.

The former paramilitary Hashed al-Shaabi coalition, part of Iraq's regular armed forces but which also includes brigades belonging to Iran-backed groups, blamed the United States for the deadliest strike so far on Iraqi territory, which killed a commander and 14 other fighters.

In the autonomous Kurdistan region, a ballistic missile attack killed six of the regional force's fighters, known as the peshmerga.

The region accused Iran of conducting the first such deadly attack on Kurdish security forces since the war began.

Neither the United States nor Iran commented on the accusations, but in a statement released late on Tuesday, Iraq said its foreign ministry would summon both representatives to "deliver formal notes of protest regarding the attacks".

It also emphasised the necessity of maintaining balanced relations both internationally and regionally to prevent Iraq being "drawn into areas of conflict".

Iraq has long been a proxy battleground for the United States and Iran, and has struggled to balance diplomatic ties with both countries.

Since the war began, pro-Iran armed groups have claimed responsibility for attacks on US interests in Iraq and across the region, while strikes have also targeted these groups, including state-linked positions.

In the statement from the prime minister's office, however, Iraq granted former paramilitaries within the official armed forces the right to "respond to military attacks" by drones and aircraft that targeted their headquarters.

- 'Decisions of war' -

Late on Tuesday, the Coordination Framework, Iraq's ruling coalition of Shia parties with varying degrees of links to Iran, backed the government decision.

However, it also condemned "attacks against state institutions and diplomatic missions", and called for the perpetrators to be punished.

The coalition said the government retained "the exclusive right of the state over decisions of war".

The Hashed al-Shaabi, also known as the Popular Mobilisation Forces (PMF), said those killed in the strike targeting its fighters included a top provincial commander.

It described the strike as a "treacherous American attack that targeted the operation headquarters", and later urged authorities to "confront these repeated American violations".

The overnight strike targeted a base in the western Anbar province bordering Syria, long the scene of operations against the Islamic State group.

Since the start of the Middle East war, Baghdad has repeatedly denounced attacks on the Hashed al-Shaabi, formed in 2014 to fight IS.

After the jihadists were defeated in 2017 in Iraq, the coalition gained influence within the security forces. Its armed factions also developed political roles, including representation in parliament, as well as economic interests.

Last week, the Pentagon acknowledged that combat helicopters had carried out strikes against pro-Iran armed groups in Iraq during the current conflict.

On Tuesday night, the sound of fighter jets was repeatedly heard in the skies above the Iraqi capital.

- Iraqi Kurdistan -

Earlier, the PMF said a "Zionist-American strike" had targeted their Mosul office in northern Iraq, with a security official saying it was a second home for coalition leader Faleh al-Fayyad, although he was not present during the attack.

The Kurdish defence ministry in the north separately said a strike targeting peshmerga forces killed six fighters and wounded 30 others, blaming the attack on Iran.

"Six Iranian ballistic missiles targeted them," said the Iraqi Kurdish authorities, branding the attack "hostile, treacherous".

Although close with Washington, Iraq's Kurds have sought to maintain neutrality in the Iran war, after relations with the Islamic republic had warmed in recent years.