The fire originated in a popular biryani restaurant in Dhaka's Bailey Road late on Thursday and quickly spread to other floors, fire service officials said.
At least 43 people have died and 22 others are being treated at hospitals with burn wounds, Health Minister Samanta Lal Sen told reporters on early on Friday after visiting the Dhaka Medical College Hospital.
"All 22 people admitted with severe burns are in critical condition," Sen added.
It was not immediately clear what caused the blaze, which was under control after two hours of effort by 13 firefighting units, fire service officials said.
Survivor Mohammad Altaf, speaking to reporters, recounted narrowly escaping the blaze through a broken window. Two of his coworkers perished, he said.
"When the fire started in the front and broke the glass, our cashier and servicemen made get everyone out. But both of them died later. I went to the kitchen, broke a window and jumped to save myself," Altaf said.
Relatives of the fire victims gathered at the hospital in the early hours of Friday to receive the bodies of their loved ones, while some were seen grieving outside the emergency department.
Many people were dining with family members including children in the building that houses mostly restaurants along with several clothing and mobile phone shops. Most of the people who perished died from suffocation and some died as they jumped off the building, doctors said.
Firefighters used cranes to rescue people from the charred building, fire service officials said.
Bangladesh Fire Service and Civil Defence Director Brigadier General Main Uddin said the fire could have originated from a gas leak or stove.
"It was a dangerous building with gas cylinders on every floor, even on the staircases," he told reporters.
A five-member committee has been formed to investigate the incident.
Intense scrutiny of Bangladesh and the major international clothing retailers that manufacture in the country has helped prevent disasters in the garment sector since a fire in 2012 and a building collapse in 2013 together killed more than 1,200 workers.
But in other industries, mainly catering to Bangladesh's booming domestic economy and without an equal emphasis on safety, hundreds of people have died in fires in recent years.
Fires are common in densely populated Dhaka, which has experienced a boom in new buildings, often constructed without adequate safety measures. Fires and explosions have occurred due to faulty gas cylinders, air conditioners and poor electrical wiring.
In July 2021, at least 54 people were killed including many children at a food processing factory outside Dhaka.
A fire that engulfed a centuries-old area of Dhaka killed at least 70 people in February 2019.