The cause was not immediately known but one survivor told AFP an air conditioner had exploded.
Ambulances were still ferrying casualties to hospitals as late as 4am local time, filling the wards of a hospital in Kut, about 160km southeast of Baghdad.
An AFP correspondent said the mall had only opened five days earlier and reported seeing charred bodies at the hospital.
The fire has since been contained but firefighters were continuing to search for missing victims.
Videos shared on social media showed distraught relatives waiting at the hospital for news, with some collapsing in grief.
One man was seen sitting on the ground, pounding his chest and crying out, “Oh my father, oh my heart”.
Dozens of people gathered in front of the hospital checking ambulances as they arrived, and some of them collapsing on the floor in agony.
‘We couldn’t escape’
One of them, Nasir al-Quraishi, a doctor in his 50s, said he lost five family members in the fire.
“A disaster has befallen us,” he told AFP. “We went to the mall to have some food, eat dinner and escape power cuts at home.
“An air conditioner exploded on the second floor and then the fire erupted and we couldn’t escape.”
Miyahi declared three days of mourning and said local authorities would file a lawsuit against the mall’s owner and the building contractor.
An investigation into the cause was under way, the governor said, adding preliminary findings were expected within 48 hours.
“The tragedy is a major shock ... and requires a serious review of all safety measures,” he said.
Safety standards in Iraq’s construction sector are often disregarded and the country, whose infrastructure is in disrepair after decades of conflict, is often the scene of fatal fires and accidents.
Fires increase during the blistering summer as temperatures approach 50C.
In September 2023, a fire killed at least 100 people when it ripped through a crowded Iraqi wedding hall, sparking a panicked stampede for the exits.
In July 2021, a fire in the Covid unit of a hospital in southern Iraq killed more than 60 people.
– Agence France-Presse