Sunday's attack struck a position held by Brigade 45, a Hashed al-Shaabi unit based near Iraq's desertic western border with Syria, killing one fighter and severely wounding a second.

"An investigation is ongoing now to determine what happened with the strike," Iraq's military spokesman Yehya Rasool told AFP.

But the Hashed, a powerful paramilitary force that fights alongside Iraq's military, was quick to blame Israel in a statement on Sunday.

It said two Israeli drones had targeted the Brigade 45 position near Al-Qaim, about 15 kilometres (10 miles) from the border, with US air cover.

The attack killed Kazem Mohsen, Brigade 45's "logistical support chief" who was also known by his nom de guerre Abu Ali al-Dabi.

Hundreds mourned at a funeral procession for Mohsen in Baghdad on Monday morning, including Ahmad al-Assadi, a member of parliament and spokesman for the Hashed's parliamentary bloc "Fatah."

"We will work in the coming days to hold an emergency parliamentary meeting to discuss this issue and take the appropriate decisions," he said in a video published by the Hashed.

- 'Declaration of war' -

Sunday's attack is the sixth in a string of blasts and drone sightings at Hashed bases across Iraq since mid-July, for which no one has claimed responsibility.

The Iraqi government has carried out investigations into some of those incidents, blaming an unidentified drone for at least one and saying another was a "premeditated" act.

It has not made any specific accusations or published the full results of the probes.

The foreign ministry said it would wait for official conclusions before taking action at the United Nations.

"If it was proven that a foreign entity was involved in these operations, we will take all steps -- first among them, going to the Security Council and the United Nations," spokesman Ahmad Sahhaf said.

Hashed deputy chief Abu Mehdi al-Muhandis, whose virulent anti-Americanism earned him a US terror blacklisting, unequivocally blamed the US last week.

But Sunday's attack was the first time the network of armed groups directly accused Israel.

Its political wing in parliament, the Fatah bloc, "strongly condemned" the raid.

"We consider this attack a declaration of war on Iraq, its people and its national sovereignty," it said.

The Hashed was established in 2014 from disparate armed groups and volunteers to fight the Islamic State group, which had swept through a third of Iraqi territory.

It operates officially under Iraq's armed forces and uses military unit names, but the US and Israel both fear that some units are an extension of their arch-foe Iran.

- Iraq, and a hard place -

The US has been implementing a "maximum pressure" campaign against Iran since withdrawing from the landmark nuclear deal with the country last year.

The Pentagon has denied involvement in the attacks and Israel has yet to confirm any responsibility, although Israeli Prime Minister Benjamin Netanyahu has said he would "act against (Iran) whenever necessary".

Among Israel's top fears is that Iran could transfer rockets to allies in Iraq, Syria and Lebanon that could ultimately be used to target Israeli territory.

It has admitted carrying out several hundred bombing raids against Iranian forces and their allies in war-torn Syria, including this weekend near Damascus to prevent an alleged drone attack.

But it also stands accused of expanding its bombing campaign to Lebanon, where Hezbollah said a pair of drones targeted the Shiite movement's Beirut stronghold early Sunday.

And on Monday, a pro-Syrian Palestinian group accused Israel of carrying out a drone attack on one of its positions in east Lebanon.