A police officer was killed and seven others wounded during clashes between supporters of Muqtada al-Sadr
and security forces, Baghdad's security operations command said Saturday.
The cleric has called for the reform of Iraq's election commission, which he has accused of corruption, and demonstrators had gathered to support him.
The rally reached the edge of the fortified Green Zone
, an area housing government buildings and foreign embassies.
Video of the rally showed police firing tear gas at the protesters.
In a statement issued after the clashes, Sadr accused security forces of using excessive force against unarmed demonstrators. The cleric also called for human rights organizations to intervene and blamed Prime Minister Haider al-Abadi for the violence.
Abadi issued his own statement, stressing the rights of Iraqis to peacefully protest, but calling for public order. He also ordered an investigation into the violence and vowed to arrest those responsible.
The United Nations Assistance Mission for Iraq welcomed Abadi's investigation and called for restraint from all sides.
"The right of freedom of peaceful assembly is the cornerstone of democracy and must be respected and protected by citizens, government and security forces at all times and in all circumstances," the mission said.
Later Saturday, rockets fired from eastern Baghdad landed inside the Green Zone, Iraq's Joint Operations Command Center said, but it's unclear whether that incident was related to the protests. There were no reports of casualties in the rocket firing.