Eight people were shot dead on Monday with a further five killed on Tuesday, including one who was fired upon during the funeral of another victim who had died hours earlier.
A protester was killed as authorities opened fire on a sit-down blockade of the main Gulf port of Umm Qasr, south of the oil city of Basra.
Officials had imposed a curfew from 10pm in Basra to disperse the demonstration and warned that they would use force if necessary.
More than 260 people have been killed since the anti-government protests began last month in Baghdad and several southern cities.
Prime Minister Adil Abdul-Mahdi offered to resign once a replacement is found.
But demonstrations are calling for fresh elections and a new type of government.
United Nations envoy for Iraq Jeanine Hennis-Plasschaert condemned the violence and called for talks in a bid to resolve the deepening crisis.
“Appalled by continued bloodshed in Iraq,” she wrote in a Twitter post.
“Violence only begets violence, peaceful demonstrators must be protected.
It is high time for national dialogue.”