Many anti-government demonstrators on Sunday rejected Iraq’s new prime minister-designate following his nomination by rival government factions, compounding the challenges he'll have to surmount in order to resolve months of civil unrest.

Meanwhile, new divisions emerged among protesters and supporters of a maverick and often inscrutable Shiite cleric, who initially threw his weight behind the uprising but now is re-positioning himself toward the political establishment, after elites selected a candidate for prime minister that he endorsed.

On Sunday, Muqtada al-Sadr told his followers camped out among protesters in the capital and in the country’s south to unblock roads and restore normalcy, angering protesters who felt al-Sadr had betrayed them and the reformist aims of their movement for political gain.

Saturday's selection of former Communications Minister Mohammed Allawi, to replace outgoing Prime Minister Adel Abdul-Mahdi was the product of months of back-room talks between rival parties, ending a political stalemate.

Hundreds of students voiced their rejection of Mr. Allawi at rallies in Baghdad's central plazas and in southern Iraq. Protesters hung portraits of Mr. Allawi marked with an “X” on bridges and tunnels around Tahrir Square, the epicenter of the four-month protest movement.

“We don't want Allawi because he is a party member chosen by the parties,” said Hadi Safir, a protester in Tahrir. “We want an independent nominee.”

Others were more diplomatic, saying they'll wait and see how Mr. Allawi delivers on promises to hold early elections.

Iraqi officials said it was likely Mr. Allawi would face the same political realities that bedeviled his predecessor, who was often caught between rival political blocs Sairoon, headed by Mr. al-Sadr, and Fatah, headed by Hadi al-Ameri.

“He is not known as being tough or outspoken, so some see him as an even more pacified version of Adil Abdul-Mahdi, and will just serve the will of the parties,” said one Iraqi official. The officials spoke on condition of anonymity because they were not authorized to speak to reporters.

But Mr. Allawi will have to cope with shifting sands of power in the Iraqi arena, with Mr. al-Sadr currently gaining the upper hand after showing his dominance over the Iraqi street. The cleric recently staged an anti-U.S. rally that brought tens of thousands to the street. By asking his followers to return to Tahrir Square, Mr. al-Sadr gained an advantage in the negotiations for prime minister.

“The groups we call pro-Iranian ... are taking a backseat now as al-Sadr emerges as more active in shaping the new government,” said Harith Hasan, a senior fellow at the Carnegie Middle East Center.

Following the U.S. airstrike in Baghdad that killed top Iranian general Qassem Soleimani, Mr. Hasan said “the conviction increased that (Iraq's) military apparatus and militias would be unable to put an end to the protest movement and at the same time secure a new deal for the new prime minister without that help of al-Sadr – that strengthened his position.”

Student demonstrations were also held in the southern city of Basra rejecting Mr. Allawi's candidacy. Other protesters burned tires in the holy city of Najaf.

“We did not choose this person; we demanded certain qualifications," said Ahmed Ali, a protester in Basra. “Mohammed Allawi is rejected by the people."

Mass anti-government protests erupted on Oct. 1 in Baghdad and the predominately Shiite south. They have decried rampant government corruption, poor services, and lack of employment; and came with lofty goals: overthrow the political establishment, pass electoral reforms, and hold snap elections. Security forces have killed at least 500 protesters since.

Mr. al-Sadr's followers returned to the demonstration camps on Friday after the cleric reversed his decision to stop supporting the protest movement.

Upon returning, Mr. al-Sadr's followers consolidated control of strategic areas in Tahrir Square, including key bridges leading to the fortified Green Zone, the seat of government. Significantly, they also moved into a skeletal high-rise building nicknamed the “Turkish Restaurant,” which offers a strategic lookout over the protests.

Militiamen interviewed said they had come to clear the area of “trouble-makers” and drug-users.

“We came here to clean this place up,” said one militia member, standing guard outside the building.

Many protesters said Mr. al-Sadr's followers had threatened them to toe the cleric's line or leave the square.

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“They will never mix with us,” said protester Mariam Nael, 18. “We are here for our homeland, they are blindly following the tweet of one cleric.”

This story was reported by The Associated Press.