Iraq has made "great efforts" in investigating attacks against demonstrators, its minister of justice said on Tuesday as teachers announced a general strike to try to revive the mass protest movement.
At least 319 people have been killed since the protests against political corruption, unemployment and poor public services began on October 1.
“We deeply regret the number of people killed and we reject the excessive violence used on protesters,” Farouq Othman said.
Iraqi leaders vowed to hold accountable those who used excessive forces against civilians, but protesters made it clear that officials were not serious about bringing in reforms.
They said the demonstrations would continue until they saw solid changes.
On Tuesday, US Secretary of State Mike Pompeo spoke with Iraqi Prime Minister Adel Abdul Mahdi and urged him to take "immediate steps to address the protesters' legitimate grievances".
Mr Pompeo called on Mr Abdul Mahdi to enact reforms and tackle corruption, State Department spokeswoman Morgan Ortagus said.
"The Secretary deplored the death toll among the protesters as a result of the government of Iraq's crackdown and use of lethal force," Ms Ortagus said.
"Secretary Pompeo emphasised that peaceful public demonstrations are a fundamental element of all democracies."
In Baghdad, schoolchildren skipped class on Tuesday and moved towards the main protest area of Tahrir Square.
“Our country is more dear to me than my only child,” read a sign hanging inside the square.
Hundreds of people also took to the streets in the southern city of Kut on Tuesday, shutting down schools and public offices to voice their anger at the government.
Most of the schools in the south were closed on Tuesday while government offices reduced their working hours.
Iraqi President Barham Salih submitted a draft electoral law to the government on Monday.
The draft called for a 30 per cent reduction in the number of parliamentary seats, from 329 to 222, and an increase in the number of voting districts.
The reforms include lowering the minimum age of candidates from 30 to 25 years.
Political appointees on Iraq’s Independent High Electoral Commission would be replaced by technocrats and judges.
The draft also stipulates that electoral reforms should allow more young people to take part in politics, to break the political cycle that has prevailed since 2003.
It remains to be seen whether these changes will calm public anger.
But Iraq’s top Shiite cleric, Grand Ayatollah Ali Al Sistani, cast doubt on the pledges made by officials.
“His eminence made clear the importance of enacting serious reform within a reasonable time frame,” his office said on Monday.
Mr Al Sistani urged said protesters should not go home until concrete steps had been shown to address their demands.
He only speaks on politics during times of crisis and has enormous influence over public opinion.
Mr Al Sistani met the UN’s top envoy to Iraq, Jeanine Hennis-Plasschaert, in the city of Najaf to discuss a path to end the protests and list a series of reforms.
“The marjaiyah [Mr Al Sistani's authority] made it clear that it supports the conduct of serious reforms in a reasonable period of time," Ms Hennis-Plasschaert said.
"Within that context, it welcomes the proposals of the UN, including the proposal for one consolidated electoral framework."
She said the UN would monitor the government's progress to ensure measures were being "done promptly, swiftly and decisively because this country needs to move forward".