Iraq's military admitted for the first time on Monday it had used "excessive force" in nearly a week of deadly protests, as paramilitary units said they were ready to back the government.

More than 100 people have been killed and several thousand wounded in demonstrations increasingly spiralling into violence, with witnesses reporting security forces using water cannons, tear gas and live rounds.

On Sunday evening, a mass protest in Sadr City in east Baghdad led to clashes that medics and security forces said left 13 people dead.

In videos distributed on social media, protesters could be seen ducking into streets littered with burning tyres as a volley of gunfire and suspected heavy weapons were heard.

"Excessive force outside the rules of engagement was used and we have begun to hold accountable those commanding officers who carried out these wrong acts," the military said.

It said Prime Minister Adel Abdel Mahdi had ordered those forces to be replaced with federal police units and the intelligence services to open an investigation into the incident.

It was the first time since protests broke out that security forces acknowledged using disproportionate measures, after the premier insisted they had been acting "within international standards" in dealing with demonstrations.

Across Baghdad on Monday morning as in several southern cities, streets were reopening and no protests could be seen, although demonstrators typically gather in the late evening.

Reform pledges

Sadr City, a densely populated, impoverished part of the capital, is a bastion of firebrand cleric Moqtada Sadr who has thrown his weight behind the protests by calling on Abdel Mahdi's government to resign.

But the embattled premier instead announced a series of reforms to create jobs, boost social welfare and oust corrupt officials.

He has accused "saboteurs" of infiltrating the protests, a claim echoed by the Hashed al-Shaabi, a powerful network of mostly-Shia, pro-Iran paramilitary units.

"We know who stands behind these protests. The plan to bring down the regime has failed," its chief Faleh al-Fayyadh told journalists in Baghdad.

He said his forces would support actions against corrupt institutions but not "the fall of the regime", a chant which has featured more prominently in the protests in recent days.

"Those who wanted to defame Iraq will be punished," Fayyadh said, adding that his forces were "ready for any government order".

His words echoed a statement earlier Monday by Iran's supreme leader Ayatollah Ali Khamenei, who accused "enemies" of trying to drive a wedge between Tehran and Baghdad.

"Enemies seek to sow discord but they've failed & their conspiracy won't be effective," Khamenei was quoted as saying on his office's Twitter account.

Iran has urged its citizens planning to take part in a major Shia pilgrimage in Iraq to delay their travel into the country over the violence.

Baghdad has close but complicated ties with Tehran, which enjoys significant influence among its Shia political groups, but is also an ally of Washington.

On Monday, Abdel Mahdi said he discussed the recent events and reform plans in a phone call with US Secretary of State Mike Pompeo, without providing further details.

And Russian Foreign Minister Sergei Lavrov landed in Baghdad to meet top officials.