"They targeted administration offices, a (Hashed) hospital, they struck forces tasked with protecting the borders," Faleh al-Fayyad said at a funeral ceremony for members of the group killed in the US strikes.

"Targeting the Hashed al-Shaabi is playing with fire," he warned.

On Friday US strikes in the west of Iraq struck positions manned by pro-Iran groups, in response to an attack in January on a base in Jordan that killed three US soldiers.

The Hashed al-Shaabi, mainly pro-Iran paramilitaries now integrated into Iraq's regular security forces, said 16 of its fighters were killed in Friday's strikes and 36 people wounded.

"We urge the prime minister to do everything in his power to defend the sovereignty and dignity of Iraq. And this can only be done with the departure of all coalition forces from Iraq," Fayyad said.

The US-led coalition was set up in 2014 to fight the Islamic State group that had seized swathes of Iraq and neighbouring Syria, and Hashed had contributed to the defeat of the jihadists in Iraq.

There are roughly 2,500 US troops deployed in Iraq and about 900 in Syria as part of the coalition.

Tensions between the US and Iraqi governments have deepened in recent months after Washington carried out previous strikes in response to a flurry of attacks on US-led troops since the Israel-Hamas war in Gaza began in October.

Washington and Baghdad opened talks on the future of the US-led troop presence late last month after repeated demands from Iraqi Prime Minister Mohamed Shia al-Sudani for a timetable for their withdrawal.