Iraqi security forces opened fire on thousands of demonstrators who defied a curfew in Baghdad on Thursday and exchanged fire with gunmen in a southern city, killing two people on the third day of nationwide anti-government protests.

The ongoing protests, in which over 20 have now been killed and 600 wounded, began over unemployment and poor services but have escalated into calls for a change of government and pose one of the worst security challenges in years.

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They appear to be independent of any political party and seemingly took the security forces by surprise.

"The bullets do not scare us. They do not scare Iraqis. This will all come down over their heads," said one protester in the capital.

At least 4,000 protesters gathered in Baghdad's Tayaran Square and attempted to march onto the central Tahrir Square only to be met with open fire and heavy tear gas.

Anti-government protesters have burned armoured police vehicles in Baghdad, Iraq. Credit: AP

Police used live ammunition in the Zaafaraniya district of Baghdad, where a protester was shot dead, and there were protests in the north-western Shula district.

Police said protesters had fired at them in the town of Rifaen near the southern city of Nassiriya where seven people were killed overnight and one more was killed on Thursday.

In the video below: Shots fired as deadly Iraq protests resume despite curfew

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Fifty people were wounded in Rifae, including five police, they said. Four people were killed in clashes overnight in another southern city, Amara.

Amnesty International called on the government to rein in the security forces and investigate the killings.

The United Nations has urged the government to "exercise maximum restraint" and allow peaceful protests.

The demonstrations began in Baghdad on Tuesday and quickly grew and spread to other cities, mainly in Iraq's south.

Protesters have been directing their anger at a government and political class they say is corrupt and doing nothing to improve their lives.