The exact sequence of the attack in the Baghdad al-Jadida area of the Iraqi capital was not immediately clear but security officials and an AFP reporter described scenes of chaos.
The attack, which IS claimed in a statement posted online, was a departure from the jihadist organisation's usual modus operandi of suicide car bombings.
According to an official from the interior ministry, gunmen blew up at least one car bomb before spraying gunfire in the street and storming a mall called Zahrat Baghdad.
Several people were held hostage inside the mall and three of them were killed as security forces attempted to neutralise the attackers, a police colonel said.
"When the security forces got too close, they killed three hostages," he said.
"The attackers at one stage released at least nine hostages, women and children," he also said.
The police officer said at least two members of the security forces were killed during the attack and nine wounded, including three officers.
A hospital official confirmed the death toll and said at least three attackers either killed themselves or were killed by the security forces.
The area around the mall, located in a busy commercial area of Baghdad al-Jadida, a populous Shiite-majority area on the eastern edge of the Iraqi capital, suffered extensive damage.
Police said a counter-terrorism force from the intelligence services was deployed to the scene of the attack.
"The security forces are now fully in control, the gunmen have been killed and the hostages have been freed," the police officer said.
Helicopters flew overhead as security forces searched the scene and the roads gradually reopened.
It said one of the IS members blew himself up in an explosives-laden vehicle when "the apostates sent reinforcements".
IS claimed that a total of 90 people were killed or wounded but the group has exaggerated the number of casualties caused by its attacks in previous such statements.
IS has suffered a number of military setbacks across Iraq in the past year. Security officials say fierce battles and relentless air strikes have depleted its manpower.
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