More than 330 people have died since October 1 in rallies in Baghdad and cities across the south calling for an overhaul of the current government, making them Iraq's deadliest demonstrations in decades.

"While the events of the last six weeks are an absolute tragedy, NATO continues to urge restraint to the government of Iraq," said Canadian Major General Dany Fortin, the outgoing commander of NATO's Iraq mission.

The year-old operation advises and trains Iraqi troops at three military schools, but Fortin said it did not have a mandate to train forces in crowd control.

Iraqi security forces have come under fierce criticism in recent weeks over their use of live rounds, machine gun fire and tear gas in response to protests.

They have been accused of firing tear gas canisters at point-blank range, leading to "gruesome" deaths and injuries when canisters pierce protesters' skulls or lungs.

Iraq's security forces include traditional military troops and federal police, as well as the Hashed al-Shaabi paramilitary network, whose various factions have been ordered to integrate into the state structure.

The military had "atrophied" following a bloody fight to defeat Islamic State group jihadists, said Fortin, describing efforts to reform it as "a generational issue".

"That takes 20 to 30 years. You're not going to see change in one year," he said.

Iraq's army was dissolved after the United States-led invasion of 2003 that toppled then-dictator Saddam Hussein.

The US then spent more than a decade helping restructure the military and the rest of Iraq's state institutions.

US, European, NATO and other forces are still deployed across Iraq to train security forces.

Fortin said NATO's operations had suffered "setbacks" in recent months, including from the protests and escalating US-Iran tensions.

Iraq has been trapped between its top two allies Tehran and Washington, who have long been at odds over the former's nuclear ambitions.

The alliance's chief, Jens Stoltenberg, told AFP in September that Tehran had been "destabilising" the region.

Fortin will be replaced at the end of November by Major-General Jennie Carignan, who will lead roughly 580 personnel, including from non-NATO partners such as Australia, Sweden and Finland.