About 50 other people were injured and the fire in Dhaka was not yet under control completely.
The Chawkbazar area where the fire was burning is crammed with buildings separated by narrow alleys. The neighborhood is a mix of residential and commercial, with buildings that commonly have shops, restaurants or warehouses on the ground floors.
The blaze started late Wednesday night in one building but quickly spread to others, fire department Director General Brig. Gen. Ali Ahmed said.
He said rescuers have recovered at least 45 bodies as they worked to get the blaze under control.
Some floors of the destroyed buildings had chemicals and plastic in storage.
Most buildings are used both for residential and commercial purposes despite warnings of the potential for high fatalities from fires after one had killed at least 123 people in 2010. Authorities had promised to bring the buildings under regulations and remove chemical warehouses from the residential buildings.
The death toll could still rise as the condition of some of the injured people was critical, said Samanta Lal Sen, head of a burn unit of the Dhaka Medical College Hospital.
Sen said at least nine of the critically injured people were being treated in his unit.
Witnesses told local TV stations that many gas cylinders stored in the buildings continued to explode one after another. They said the fire also set off explosions in fuel tanks of some of the vehicles that got stuck in traffic in front of the destroyed buildings.