Sulaymaniya has been witnessing protests for many weeks.
Thousands of people have joined the demonstrations to protest against corruption and a lack of social services.
Sunday once again the protest ended in terror, with police firing shots, using tear gas and batons to disperse the protesters.
Seven protesters also suffered bullet wounds and some others were hurt by batons or tear gas, Reuters quoted police and witnesses as saying. At least 35 people have been reported wounded.
Several people were also taken into custody, including journalists.
Two journalists were among the wounded, one of them a photographer, who was shot while covering the clashes, said Rahman Gharib, an editor at the Kurdish weekly newspaper Hawalati, said sources in Kurdistan Region.
Kurdistan is dominated by two parties, the PUK and the regional president's Kurdistan Democratic Party (KDP).
President of Iraq's Kurdistan region Massoud Barzani had announced plans last month to shake up the regional government and enact reforms, but demonstrators wanted more reforms.