At least 84 protesters were killed, a lot of them in Baghdad, since Tuesday when demonstrators initiated rallies to demand jobs, improvements to services and an end to corruption in the oil-rich nation.
Prime Minister Adel Abdul Mahdi's 17-point plan was the result of an emergency cabinet meeting on Saturday night and comes after days of offering only vague reform promises.
The two officials said the security forces responded with fire, but there was no immediate word on casualties.
The protesters, mostly young men, were scattered in side streets near Sadr City on Sunday afternoon.
Security forces have beefed up their presence in central Baghdad, deploying as far as Sadr City to seal off Tahrir Square. Soldiers fired toward the protesters to push them back. After about an hour, there was more intense gunfire as protesters persisted in trying to advance. One protester carrying a drum chanted "peaceful, peaceful", as others joined in.
The clashes have revived fears of a new spiral of violence that could suck in influential militia groups and be exploited by Islamic State in Iraq and Syria (ISIS).
Abdul Mahdi's office and Parliament Speaker Mohammed al-Halbusi have called on protest representatives to meet with them so they could hear their demands.
Two years after the defeat of Daesh, security is better than it has been in years, but corruption is rampant, wrecked infrastructure has not been rebuilt and jobs remain scarce. Iraq is allied with both countries and hosts thousands of USA troops, as well as powerful paramilitary forces allied with Iran.
Almost 4,000 people have been injured and 93 were killed during the heavy crackdown against protesters over the past few days, according to the Iraqi parliament's human rights committee.
She described the violence as a "senseless loss of life" and said those behind it must be held accountable.
"Five days of reported deaths and injuries: this must stop", said the United Nations' top official in Iraq, Jeanine Hennis-Plasschaert. He said the violence has been "reciprocated".
He said an investigation is underway to determine the source of live fire that killed many of those who have died in the unrest.
But Abdul-Mahdi may already be too late as protests continue.
Elsewhere, angry protesters torched the offices of political parties in the southern province of Dhi Qar, witnesses said.
Protests were met with tear gas and gunshots from security forces, followed by a curfew in the capital and elsewhere.
He announced a list of executive decisions focusing on providing housing for those on low incomes, unemployment benefits and vocational training.
Demonstrators disperse as Iraqi security forces use tear gas during a protest over unemployment, corruption and poor public services, in Baghdad, Iraq on october 2, 2019.
Sadr's movement has the power and organisation to bring large numbers of supporters onto the streets, but at the risk of alienating many of those whose protests in recent days have been based on rejecting all of Iraq's feuding political factions. Students made it to schools and government employees returned to work.
"The protests are making people afraid to go out", he said, estimating his sales to have dropped by 70 percent.
In a desperate attempt to curb the growing rallies, authorities blocked the internet and imposed an around-the-clock curfew in the capital. On Saturday, in the southern cities of Nasiriyah and Diwaniyah, protesters defied curfew still in place there. One square where protesters had gathered in their hundreds in previous was packed with hundreds of policemen and other security personnel.
Never miss the latest news from the Star. Both of those stations are privately owned. In a surprise shift of stance from his tactics over previous years, he has not called his followers to support the protests and provide protection for them.