The blaze broke out late on Saturday in the multi-floor Tazreen Fashion factory in the Ashulia district on the outskirts of the capital Dhaka.
Some people died after jumping from the building to escape the flames.
It is unclear what caused the fire, which started on the ground floor trapping many victims in the factory.
Officials suspect an electrical short circuit might have caused the disaster.
Firefighters managed to contain the blaze on Sunday morning.
Fatal fires are common in Bangladesh’s large garment manufacturing sector and Western companies are likely to renew pressure on the local businesses to improve safety.
In a separate development, at least 13 people died when a flyover under construction collapsed late on Saturday in the south-eastern city of Chittagong, police said.
The authorities are investigating both accidents.
Initial reports said eight people had been killed in the factory fire, but the scale of the disaster became clear when rescue workers entered the building on Sunday.
“We resumed our search this morning and found the bodies lying on different floors of the factory building,” Brigadier General Abu Nayeem Mohammad Shahidullah of the Dhaka fire brigade told AFP news agency.
Later reports said that 120 people had died, but the number of fatalities was then lowered to at least 112. A number of people are believed to be missing.
The fire started on the ground floor – which was reportedly used as a warehouse – and quickly spread through the building.
Senior fire department official Mohammad Mahbub told the Associated Press news agency that the factory had no fire exit on the outside of the building.
“Had there been at least one emergency exit through outside the factory, the casualties would have been much lower,” he said.
The factory owner denied the allegations that the building was unsafe to work in.
“It is a huge loss for my staff and my factory. This is the first time we have ever had a fire at one of my seven factories,” Delwar Hossain told AFP.
Police and soldiers were deployed to keep the situation under control as thousands of anxious relatives of factory employees gathered at the scene.
“Where’s my son?” cried Sabina Yasmine. She said she saw the body of her daughter-in-law, who died in the fire, but her son was missing, AP reports.
She expressed fury at the factory owners, who she blamed for the fire.
Fatal fires are common in Bangladesh’s large garment manufacturing sector.
Lax safety standards, poor wiring and overcrowding are blamed for causing several deadly factory fires every year.
In December 2010, a wiring problem led to a fire in another clothes factory in the same industrial zone, leaving at least 25 people dead.
There are around 4,500 factories in Bangladesh, employing more than two million people.
Clothes account for up to 80% of Bangladesh’s $24 billion annual exports.
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