Authorities are still trying to establish a full death count and return identified bodies to the victims' families.
The fire started late Thursday at a restaurant on the first floor of the Green Cozy Cottage shopping centre in Dhaka.
Fire Service and Civil Defence Director General Main Uddin said more than a dozen firefighting units were deployed to douse the fire.
Firefighters rescued survivors and pulled out bodies, and by early on Friday, at least 43 people died. Health Minister Samanta Lal Sen said the toll could rise, as at least 18 critically injured people were being treated in two state-run hospitals.
One survivor said people escaped by heading to the building's roof.
“I knew about the fire when it was at the first floor. We moved to the roof of the building. Around 30 people were there. After the fire was under control, fire service personnel broke into one side of the roof and rescued us,” Mohammed Siam said.
Thirty-eight victims have been identified and 26 of the bodies have been handed to their families, said Bacchu Mia, who is in charge of a police outpost at Dhaka Medical College Hospital.
“Overnight many families waited here for their loved ones. It’s a heartbreaking scene as they desperately looked for their family members who died in the tragedy,” Mia said.
A fire department team entered the charred building in the morning to see if there were more bodies, and forensic experts began looking for evidence in the investigation of the fire.
The cause of the fire has not been determined.