Local media reported that up to 124 people were killed. The cause of the blaze was not immediately clear; authorities ordered an investigation.
Army soldiers and border guards were sent to help police keep order as thousands of onlookers and anxious relatives of the factory workers gathered, Mahbub said.
Tazreen was given a "high risk" safety rating after a May 16, 2011, audit conducted by an "ethical sourcing" assessor for Wal-Mart, according to a document posted on the Tuba Group's website. It did not specify what led to the rating.
Wal-Mart spokesman Kevin Gardner said online documents indicating an orange or "high risk" assessment after the May 2011 inspection and a yellow or "medium risk" report after an inspection in August 2011 appeared to pertain to the factory where the fire broke out. The August 2011 letter said Wal-Mart would conduct another inspection within one year. Gardner said it was not clear if that inspection had been conducted or whether the factory was still making products for Wal-Mart.
If a factory is rated "orange" three times in a two-year period, Wal-Mart won't place any orders for one year. The May 2011 report was the first orange rating for the factory.
Neither Tazreen's owner nor Tuba Group officials could be reached for comment.
The Tuba Group is a major Bangladeshi garment exporter whose clients also include Carrefour and IKEA, according to its website. Its factories export garments to the U.S., Germany, France, Italy and the Netherlands, among other countries. The Tazreen factory, which opened in 2009 and employed about 1,700 people, made polo shirts, fleece jackets and T-shirts.
Bangladesh has some 4,000 garment factories, many without proper safety measures. The country annually earns about $20 billion from exports of garment products, mainly to the U.S. and Europe.
In its 2012 Global Responsibility report, Wal-Mart said that "fire safety continues to be a key focus for brands and retailers sourcing from Bangladesh." Wal-Mart said it ceased working with 49 factories in Bangladesh in 2011 because of fire safety issues, and was working with its supplier factories to phase out production from buildings deemed high risk.
At the factory, relatives of the workers frantically looked for their loved ones. Sabina Yasmine said she saw the body of her daughter-in-law but had seen no trace of her son, who also worked there.
"Oh, Allah, where's my soul? Where's my son?" wailed Yasmine, who works at another factory in the area. "I want the factory owner to be hanged. For him, many have died, many have gone."
Mahbub said the fire broke out on the ground floor, which was used as a warehouse, and spread quickly to the upper floors. Many workers who retreated to the roof were rescued, he said. But he said that with no emergency exits leading outside the building, many victims were trapped, and firefighters recovered 69 bodies from the second floor alone.
"The factory had three staircases, and all of them were down through the ground floor," Mahbub said. "So the workers could not come out when the fire engulfed the building."
"Had there been at least one emergency exit through outside the factory, the casualties would have been much lower," he said.
Many victims were burned beyond recognition. The bodies were laid out in rows at a school nearby. Many of them were handed over to families; unclaimed victims were taken to Dhaka Medical College for identification.
Prime Minister Sheikh Hasina expressed shock at the loss of so many lives.
The Bangladesh Garment Manufacturers and Exporters Association said it would stand by the victims' families.