The Shiite cleric with a cult-like following in Iraq has thrown his weight behind the appointment of Allawi, despite the premier's rejection by a protest movement Sadr once backed.

The onetime anti-US militia leader whose supporters form the largest bloc in parliament had spent most of the past few months in neighbouring Iran but came back to whip up support for Allawi's government line-up.

As he visited the mausoleum of Imam Ali in Najaf, the Shiite shrine city where he resides, Sadr demanded that parliament approve the line-up in the coming days.

"If the session does not take place this week, or if lawmakers don't (back) a transparent Iraqi cabinet in a vote... then this will require a demonstration of a million people," he tweeted.

"Sit-ins around the Green Zone (where parliament is located) will have to be used to exert pressure," he said.

Allawi has called for a vote of confidence to be held on Monday and has been backed by his predecessor Adel Abdel Mahdi, who bowed out as prime minister in December in the face of pressure from the street.

But the constitutional position is unclear.

Deputy parliament speaker Hassan Karim al-Kaabi, who is close to Sadr, told Iraqi media that Abdel Mahdi's request for an extraordinary session to hold the confidence vote was binding.

But parliament speaker Mohammed Halbusi said he has not yet agreed to convene the session and several lawmakers from Iraq's Sunni Arab minority said they would boycott any vote.

Sadr's loyalists already paralysed the country in 2016 with massive sit-ins in front of parliament and government headquarters.

But this time, he may not be able to mobilise such large numbers, after losing favour among some of his backers for withdrawing his support from the protest movement.