BAGHDAD — Tens of thousands of angry Iraqis took to the streets to demand changes to their government Friday in a potent challenge to Prime Minister Haidar al-Abadi from his own Shiite constituency, including the country’s powerful militias. Chanting crowds thronged Baghdad’s central Tahrir Square and jammed the main streets around it, some calling on Abadi to fire corrupt ministers and others urging more sweeping changes to the entire system of governance installed after the U.S. invasion of 2003.

The protest was the biggest in a surge of demonstrations that have erupted across the country over the past week as Iraqis enduring an unusually intense heat wave vent frustration with their government, which has proved unable to provide basic services 12 years after the invasion left the country’s infrastructure smashed.

The numbers in and around Tahrir Square far exceeded a much smaller demonstration a week earlier that had been organized by an assortment of secular activist groups to protest the lack of electricity at a time when temperatures are routinely hitting 120 degrees or more.

Friday’s, in contrast, had the backing of the powerful Shiite factions whose militias are leading the fight against the Islamic State and who have increasingly been agitating for greater political power. It also had the support of the highly influential religious leader Ayatollah Ali Sistani, regarded as the voice of Shiite moderation.

In a statement issued at Friday prayers, one of Sistani’s top aides called on Abadi to do more to combat widespread corruption in his government.

“What is needed from [Abadi] is to be more daring and braver in his reforms,” said the aide, Ahmed al-Safi.

Abadi responded with a statement vowing to heed the protesters’ demands.

“I promise to announce a comprehensive reform plan,” he said in the statement.

Similarly large protests were held across the Shiite south, including in the cities of Basra, Najaf, Karbala and Nasseriyah, underscoring the building challenge to Abadi, who was appointed a year ago at the urging of the United States to bring new impetus to the fight against the Islamic State. But he has struggled to wield his authority on a government widely perceived as corrupt and ineffective, and the power of the non-state militias has further eroded his ability to act.

Some of the demonstrators called directly for Abadi’s resignation.

“You have killed our joy and stolen our dreams. We don’t want you anymore,” said one banner held aloft above the crowd, which included families and older people who said their sons were fighting with the militias.

Though all the demonstrators complained about corruption and the lack of services, there were noticeable differences in their demands, reflecting rifts emerging among Iraqi Shiites as the fight against the Islamic State unfolds.

Supporters of Qais al-Khazali, who heads the powerful Iranian-backed Asaib Ahl al-Haq militia, echoed his demand for the abolition of Iraq’s elected parliament and its replacement with a presidential system of government.

“If you think you can carry out reforms, we are with you,” Khazali said in a televised statement late Friday night. “If you think you can’t, resign.”

The protesters also included a sizable number of supporters of former prime minister Nouri al-Maliki, who suppressed similar demonstrations against the corruption of his government four years ago by detaining and intimidating organizers. Maliki, who has not attempted to hide his hopes of returning to power, issued a statement calling on Abadi “to hit corrupt officials financially and politically.”

Many demonstrators said they had turned out only to demand what Lamia Fadhil, 29, called “a decent life.”

“For more than 10 years the government didn’t provide anything for us. No electricity, no services and no jobs,” she said. “That’s it. We’ve had enough