Haque said the government had launched an investigation into the blaze, which firefighters said was fuelled by an illegal chemicals warehouse.
"The chemicals warehouse was illegally set up in the residential area. We are looking for its owner," Haque said.
The blaze burned for several hours before firefighters were able to bring it under control.
Nicholas Haque, Al Jazeera's correspondent in Dhaka, reported "chaotic scenes" at the site of the blaze.
"Hundreds, if not thousands of people are here looking for their loved ones. Police have cordoned off the area," he said on Friday.
Abu Nayeem, the fire department chief, said the fire had been caused by an electrical fault and spread rapidly before firefighters could access the area.
Many of the victims were attending a wedding on the roof of one of the buildings.
Sheikh Hasina, the country's prime minister, visited the injured and announced compensation and free treatment for the victims.
Fires due to short-circuits, substandard wiring and electrical faults are common in Bangladesh, where building regulations are rarely enforced.