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.
An Iraqi protester waves the national flag during protests on Saturday
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.
Iraq’s prime minister, Adel Abdul-Mahdi, on Saturday called on protesters to end the unrest and said he would meet them to hear their demands.
He said security forces had been ordered to only use live ammunition in strict cases of self-defence.
Also on Saturday, armed men dressed in black stormed the offices of a news broadcaster in Iraq.
The Saudi-owned Al Arabiya news channel said some of its staff had been injured and equipment destroyed in the raid, which came after days of threats to the broadcaster.
A member of staff claimed “members of the federal police declined assistance to us during the attack” but they had since had “assurances from the prime minister’s office and from officials [they will] investigate”.
Mr Maan said that authorities condemned all attacks against media outlets.
Gunmen also attacked the offices of Iraq’s privately owned Dajla and NRT news channels in Baghdad.
Iraqi protesters burn tyres during a protest on Saturday
The demonstrators are demanding the resignation of the prime minister and an investigation into the killings of protesters.
Grassroots rallies began as demonstrators, many of whom are young, took to the streets demanding jobs and an end to corruption. They also called for improvements to basic amenities including electricity and water.
