An influential Iraqi Shia cleric addressed thousands of anti-government protesters who filled the streets of downtown Baghdad on Friday, threatening to boycott the country’s upcoming provincial elections if the committee overseeing the vote is not overhauled.

Muqtada al-Sadr’s remarks reflect persistent political power struggles in Baghdad even as Iraqi forces backed by the U.S.-led international coalition battle the Islamic State group in Mosul in a weeks-long campaign to rout the extremists from the western half of the city.

Mr. Al-Sadr has repeatedly accused the committee along with all tiers of Iraq’s government of being riddled with corruption. He called for the rally in Baghdad just days before asking his followers to “stand in the face of ... corruption and tyranny,” according to a statement from his office.

Iraqis who love their country and hate corruption, regardless of ideology, support what Mr. al-Sadr called the “reform revolution.”

Nationwide protests demanding reform first erupted after IS overran nearly a third of Iraq in the summer of 2014, plunging the country into a deep political and security crisis. As the battle against IS stalled and an economic crisis deepened, a wave of largely civic and secular protests mobilized millions across Iraq in the summer of 2015.

But in the months that followed the movement lost steam. Mr. Al-Sadr picked up the mantle of reform shortly afterward and first began mobilizing thousands of his followers in the Iraqi capital the following year.

Since early 2016, Mr. al-Sadr’s protests have occasionally turned violent. Last month, clashes between protesters and security forces left at least five dead. The crowds have also twice breached Baghdad’s highly fortified Green Zone, home to the government and many foreign embassies. In one instance al-Sadr’s protesters occupied parliament, but withdrew peacefully after a call from his office to do so.

Though none of Iraqi Prime Minister Haider al-Abadi’s political opponents have emerged powerful enough to unseat him, the country’s political blocs remain capable of blocking legislation and unseating key ministers in al-Abadi’s government.

Iraq is to hold local elections later this year, the first nation-wide vote since IS overran nearly a third of the country in 2014, and Mr. al-Abadi took office shortly afterward.