It was not immediately clear what caused the fire at the building in the centuries-old Chawkbazar area of Dhaka.
Another control room official, Russel Shikder, said 81 bodies had been recovered.
A relative of one of the victims mourns outside Dhaka Medical College Hospital.
The fire broke out in a building with shops on its ground floor, a warehouse for plastics and flammable material on the first, and homes on three floors above, said Shamim Harun ur Rashid, a local police official.
Another fire official told reporters the blaze, which began around 10.40pm (16:40 GMT) on Wednesday, has been "confined" but not yet extinguished despite the efforts of more than 200 firefighters.
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Some reports suggested numerous dead were pedestrians, shoppers or diners who died quickly as several gas cylinders exploded, and the fire engulfed the nearby buildings very quickly.
The other residential buildings that caught fire may have also served as places to store plastics and chemical goods, he said. Authorities had promised to bring the buildings into line with regulations and remove chemical warehouses from the residential buildings. Crammed with tightly-packed residential and industrial buildings, some just inches apart, the district dates back to the Mughal era more than 300 years ago. "They are not really abiding by the government's rules". Hundreds of people have been killed in recent years.
"After the Nimtoli tragedy we urged our local leaders not to allow any more godowns that are a danger for us", he added, referring to a 2010 fire that killed at least 124.
Numerous factory workers had left the building for lunch at the time, but witnesses described seeing dozens of trapped workers jumping from the 10th floor of the building to escape.
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The Rana Plaza factory collapse in 2013 killed more than 1,100 workers and a fire in a garment factory in 2012 killed 112 people.
According to a fire services chief it may have been triggered by a gas cylinder.
Doctors at Dhaka Medical College Hospital said at least 55 people were injured, including 10 in a critical condition.
A second fire official said the "highly combustible" chemicals caused the blaze to intensify.
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