Rescuers dug out 15 bodies and pulled 58 people alive from the debris, but narrow roads leading to the site hampered efforts to bring in cranes to help remove concrete slabs.
Police and firefighters said the building collapsed on Monday a little after midnight while many employees were working the night shift.
The army brought in sniffer dogs and heavy equipment, including cranes, to the site by Monday afternoon.
"We will work through the night and expect to complete the rescue operation by tomorrow," one rescue official said.
Anxious relatives joined rescuers searching for survivors in the flattened remains of the building at Palashbari, 30km from Dhaka, which housed a garment factory.
"In a few minutes the entire structure crumbled like a house of cards," a witness told a private television channel.
One survivor thought at least
500 people were trapped
A massive pile of bricks and concrete slabs is all that remains of the building. Rescuers and relatives stood helplessly on top, some calling for loved ones.
"We suspect up to 500 people are under the debris. It was a packed night shift running ... and dozens may have died already," a survivor said.
Security officer Abdul Hye said at least 250 people had been working the night shift at Shahriar Fabrics.
Prime Minister Begum Khaleda Zia flew to Palashbari in the afternoon and was visibly shocked at the scale of the destruction.
"I want you to mobilise all strength and resources to speed up the rescue efforts and not to let anyone die due to negligence," the prime minister said.
"Until a few minutes
ago, my brother Jamal was calling me on my mobile for help. But now he has gone quiet"
She said the government would do everything possible to help survivors and families of the dead.
Police said the collapse was probably triggered by a boiler explosion at the factory. Fire brigade officials said they would investigate further to determine the exact cause.
Shahid Alam, a senior official of the Dhaka Development Authority, said the factory had been built on marshland without planning permission.
Prime Minister Khaleda Zia: No
one should due to negligence
State Minister for Home Affairs, Lutfuzzaman Babar, visited the scene on Monday and expressed his annoyance over what he said was its unauthorised construction.
The whereabouts of the building's owners was not immediately known.
Anxious residents used mobile phones to try to contact relatives trapped beneath the rubble.
"Until a few minutes ago, my brother Jamal was calling me on my mobile for help. But now he has gone quiet," Ruma Begum
She added: "I am still frantically trying to reach him on his mobile ... but there is no response. Only Allah knows what has happened."