UN proposes reform plan, backed by Iraq's Grand Ayatollah Ali Sistani, to end violence that has killed more than 300.
Iraqi protesters rallied and many schools stayed closed on Tuesday as the UN stepped up pressure on the government to agree to a raft of reforms.
While security forces again faced off with activists around Baghdad's Tahrir (Liberation) Square, teachers and students went on strike across much of the Shia-majority south.
The UN has proposed a reform plan that demands an immediate end to the violence that has killed more than 300 people since the start of October, as well as a host of reform measures.
The UN's top Iraq representative, Jeanine Hennis-Plasschaert, met with Iraq's top religious authority on Monday, days after influential neighbour Iran brokered a political deal to keep the ruling system in place.
Iraq's Grand Ayatollah Ali Sistani has backed the UN plan but said he feared political forces were not "serious" about enacting the required reforms.
Hennis-Plasschaert was due to attend a special parliamentary session this week in Baghdad, where demonstrators appeared bolstered by her visit.
"We're optimistic about the UN and I respect her visit to Sistani," said one demonstrator, Ali Kadhem, 33, at the main protest site of Tahrir Square.
"Let them intervene more in Iraq. We want them here. Our people were starved, killed. We've been through everything."
Security forces again sealed off Tahrir with concrete blocks, which activists had earlier pulled down, and lobbed sound grenades at teenage boys who had skipped class to protest.
"Our country is dearer to me than my only child," read one slogan daubed on a street nearby, where the usually bustling mechanics' shops remained closed amid the unrest.
Across the country's south, meanwhile, most schools were shut as teachers and students rallied.
Schools closed in the towns of Hillah and Kut, where hundreds hit the streets, and in the protest hotspots of Nasiriyah and Diwaniyah.
Young people make up 60 percent of Iraq's population of nearly 40 million, and youth unemployment stands at 25 percent, according to the World Bank.
The lack of employment is a key driving force behind the popular anger, with demonstrators accusing the government, the country's biggest employer by far, of handing out jobs based on bribes or nepotism instead of merit.
Since the protests started in early October, they have swiftly escalated into demands for a sweeping overhaul of the entire system.
But political parties appear to have rallied around the government of embattled Prime Minister Adil Abdul Mahdi.
Sources said they closed rank following meetings led by Iran's Major General Qasem Soleimani, the head of the Islamic Revolutionary Guard Corps' foreign operations arm.
Soleimani, who often appears in Baghdad at times of political crisis, brokered a deal to keep the ruling system intact, with Abdul Mahdi at its head, in exchange for some reforms.
But the UN has also upped its mediation with Iraqi actors and Hennis-Plasschaert has proposed a phased roadmap that would start with an immediate halt to the use of force.
It also calls for electoral reforms and anti-graft measures in the next two weeks, followed by constitutional amendments and major legislation on infrastructure within three months.
Sistani met with Hennis-Plasschaert on Monday and welcomed the plan, a vital endorsement in a country in which the Shia religious authority holds tremendous sway.
Sistani, who never appears in public, has described the protesters' demands as "legitimate" in his weekly Friday sermons, delivered through a representative.
His office has also denied being a party to any agreement brokered by Soleimani to keep the government in place.
Iraqi authorities have faced widespread international criticism for the mounting death toll from protest-related violence, which has exceeded 300 in six weeks.
At least 18 protesters have died since Saturday, medical sources said.
Rights defenders have complained that the government has stopped providing updated casualty figures and has severely restricted access to the internet.
Volunteer medics and activists, meanwhile, have spoken of a campaign of kidnappings, killings and intimidation they say is aimed at scaring them into stopping their work.