Protesters had feared the rallies thronging Baghdad's main protest camp of Tahrir Square could spiral into chaos, after supporters of the Hashed al-Shaabi paramilitary group flooded the area on Thursday in a show of force.

The anti-government demonstrations had been relatively calm on Friday but after night fell, armed men on pick-up trucks attacked a large building where protesters had been camped out for weeks, witnesses told AFP.

The gunmen forced young demonstrators out of the building and live rounds could be heard after the altercation.

State television said the building had been torched "by unidentified men".

Medics and police sources told AFP at least nine were shot dead and dozens of other demonstrators were wounded, expecting the toll to rise further.

One female medic at a field clinic nearby said she had treated at least five people for light knife wounds.

The new deaths bring the toll to nearly 440 dead and 20,000 wounded since anti-government rallies erupted on October 1 in Baghdad and the Shiite-majority south.

The movement is the largest and deadliest in Iraq in decades, with the mostly young protesters accusing the entrenched political elite of corruption, incompetence and being under the sway of neighbouring Iran.

- Newcomers flood Tahrir -

The United States on Friday imposed sanctions on three Iranian-backed Iraqi paramilitary leaders over a deadly crackdown against the protests, warning Tehran to stay out of its neighbour's affairs.

Iran wields tremendous sway in Iraqi political and military circles, especially within the Hashed al-Shaabi.

President Donald Trump's administration, which considers Iran an arch-enemy, has also voiced alarm at rising attacks on US forces' bases in Iraq blamed on Shiite militias backed by Tehran.

Secretary of State Mike Pompeo on Friday announced sanctions against three Iraqis, including Qais al-Khazali, leader of the prominent Asaib Ahl al-Haq brigade of the Hashed.

Two other Hashed leaders, Laith al-Khazali and Hussein Falil Aziz al-Lami, are also targeted by the measures which would seize any assets they have in the US and keep them from travelling there.

Supporters of the Hashed had startled protesters on Thursday, arriving in their thousands at the camp in Tahrir Square.

Some of the newcomers carried portraits of Hashed fighters killed battling Islamic State group jihadists, and of the country's top Shiite cleric, Grand Ayatollah Ali Sistani.

The Hashed initially backed Iraq's government against the protests, but switched to supporting the rallies after an intervention by Sistani.

But protesters were apprehensive about its sudden influx into Tahrir and on Friday erected new checkpoints around the square to search new arrivals.

The rallies were relatively peaceful, attracting hundreds of clerics and officials from Shiite shrines in Baghdad, Karbala, Najaf and other cities.

With robed clerics in white turbans leading the way, a procession circled through Tahrir, carrying signs reading "The marjaiyah (Shiite religious leadership) is our support!"

"This is in support of our brothers protesting in Tahrir," said Fadel Oz, an official from the revered Karbala shrine.

One protester told AFP their presence made it less likely the rallies would descend into clashes.

"The religious shrines' involvement grants legitimacy and numbers to the protests," said Thaer Istayfi, 41.

Protesters had long complained of being closely monitored and harassed in Tahrir Square, and rights groups have urged authorities do more to protect activists.

On Friday, relatives of Zeid al-Khafaji, a 22-year-old photographer, said he had been kidnapped whilst returning from Tahrir.

That came after the bruised body of 19-year-old Zahra Ali was left outside her family home after she went missing, her father said.

- Search for new PM -

A deadly crackdown last week prompted a dramatic intervention by Sistani that led to the resignation of Adel Abdel Mahdi.

Sistani insisted on Friday that the religious leadership was not involved in talks on his replacement.

"The marjaiyah is not party to any discussions on this and has no role in any way whatsoever," he said, in a sermon read by his representative in the shrine city of Karbala.

He did however urge that a new premier be selected within 15 days, as per the constitution, and with no "foreign interference."

A senior political source told AFP that Iran's pointman for Iraq, Major General Qasem Soleimani, has been attending the talks.

David Schenker, the top US diplomat for the Middle East, on Friday echoed Pompeo's remarks, slamming Soleimani's presence.

"It is unorthodox and it is incredibly problematic and it is a huge violation of Iraqi sovereignty," Schenker told reporters, urging Iraq's neighbours "not to meddle".