At least 13 people were killed during protests last week. Demonstrators called for better jobs and improvements in basic government services like electricity.
Iraqi Prime Minister Nouri al-Maliki gave his ministers 100 days to address the demands or be removed from their posts, CNN International reports.
Shiite cleric Moqtada Sadr said in a letter addressed to Maliki that the prime minister is the man responsible for tackling reforms, however.
"What is happening in Iraq is part of the prime minister's basic responsibility, which he can't ignore, in front of God almighty and the people," he was quoted by the Voice of Iraq news agency as saying.
Sadr last week joined Shiite Grand Ayatollah Ali Sistani in urging demonstrators to stay home, a sentiment backed by the prime minister.
Human Rights Watch, meanwhile, called on Baghdad to investigate reports that national security forces fired on protesters during Friday's unrest.
"The Iraqi authorities need to rein in their security forces and account for every single killing," said Tom Porteous, deputy program director for Human Rights Watch, in a statement. "The security forces need to use the maximum possible restraint in dealing with protesters."