Eight of the dead are members of the government's security forces.
Contradicting many eyewitness reports, spokesman Saad Maan told Iraqi television that no government forces had fired directly at protesters.
Soldiers were seen firing in the direction of about 300 anti-government protesters in a suburb of the capital Baghdad on Sunday, the sixth day of demonstrations.
During the week, soldiers have been seen using tear gas and live ammunition.
As well as the 6,107 protesters injured, Mr Maan said more than 1,200 members of the security forces had also been wounded during the demonstrations that have taken place across Baghdad and the south of the country since Tuesday.
It is the most serious disruption to hit the country since the defeat of Islamic State two years ago.
