Firefighters were called to the neighbourhood of Cocody shortly after midnight. Four bodies had been recovered from the rubble by mid-morning, the fire brigade said on Facebook.
Thirty people were carried out alive, 13 of whom were taken to hospital, it said. The number of people in the building when it collapsed was not immediately clear.
Photos from the scene showed rescue workers using torches to search through a giant pile of cement and debris. One fire fighter cradled a baby in the back of an ambulance.
Prime Minister Patrick Achi visited the site and paid tribute to the victims, a Reuters reporter said.
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The cause of the accident was not immediately clear.
Several people were killed in the collapse of a building in the Abidjan neighbourhood of Treichville last month, according to local media.
(Reporting by Loucoumane Coulibaly and Ange Aboa; Writing by Sofia Christensen; Editing by Nellie Peyton and Nick Macfie)
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