Hundreds more people were injured in what are the second wave of protests in October.
The protesters, mainly unemployed young men, are calling for work, better public services and an end to corruption in their country.
They blame Prime Minister Adel Abdul Mahdi’s government and Iranian-backed Shia militia groups for the continuation of years of poverty.
On Saturday, Mr Abdul Mahdi deployed members of the country’s counter-terrorism service (CTS) in an effort to contain violence in the capital Baghdad and the city of Nasiriya in the south.
They were instructed to “use all necessary measures” to end the demonstrations, news agency Reuters reported.
The CTS took over checkpoints around Baghdad’s central Tahrir Square after tear gas fired by security forces failed to clear the area of protesters.
Four people died after being struck on the head by tear gas canisters.
In Nasiriya the counter-terrorism officers attacked and arrested dozens of protesters, according to police and security sources. Four protesters were shot dead after they tried to set fire to the office of a security official, police said.
Seven others died after the Badr Organisation militia shot at protesters near their office. The group is backed by Iran, which has ties to many of Iraq’s political parties.
Protester Silwan Ali, 33, said: “Our protests are peaceful, we only have flags and water bottles, but they keep firing bombs at us, firing tear gas at us.
“What have we done to deserve this? What have we done? The young men who died, what did they do?”
Another protester, who would not give his name, said: “The government has been stealing from us for 15 years.
“Saddam went and 1,000 Saddams have been hiding in the Green Zone,” he added, meaning the former Iraqi dictator.
“I want change,” said Fares Mukhaled, 19. “I want to remove those corrupt people who sleep in the Green Zone and who fired tear gas and rubber bullets at us.”
The heavily-fortified Green Zone is home to embassies and government offices.
A parliamentary discussion of the protests, scheduled for Saturday, was cancelled after failing to reach a quorum, with many politicians staying home to avoid the violence.
Iraq was occupied by western forces after the US-led invasion in 2003 and until 2017. It also suffered under an Islamic State insurgency but the past two years had been relatively stable.
Mr Abdul Mahdi took office a year ago, promising reforms but the protesters say their lives have not improved.
In the first wave of protests earlier this month, 157 people were killed and more than 6,000 injured.