Brigadier-General Nizam Ahmed, who was overseeing the operation, told The Associated Press rescue workers had pulled 13 bodies from the rubble of the building in Dhaka's central Tejgaon industrial district.
Another two died on the way to hospital on Saturday, Ahmed said.
Mizanur Rahman, who lives nearby, said most of those injured or killed appeared to be construction workers who were adding a new storey to the building, which was being converted into a 500-bed medical centre.
Witnesses said passing pedestrians were also among the victims, which included dozens of injured who were taken to hospital.
More than two dozen tin-roofed, one-room shanty homes were also buried by the 1800 square metre building as it collapsed, Ahmed said.
Slum dwellers trapped
Rescuers feared a dozen slum dwellers, mainly family members of day labourers who were working elsewhere at the time, were trapped inside.
Soldiers and fire fighters used bulldozers, hammers and crowbars to clear and sift through the rubble of the building, looking for survivors or bodies.
Most of those killed or injured
were construction workers
Ahmed said: "We are working very carefully so no trapped survivor is hurt."
Munir Hossain, a physician who treated a dozen of those critically injured at a nearby hospital, said many of the injured survivors may need to have their legs or hands amputated.
Rahman said a garment factory had moved out of the building last month, but some of its staff were there to complete the move.
Witnesses estimated there were about 100 people inside the building when it collapsed, some of them operating small convenience shops on the ground floor.
The owner of the building was not available for comment.
On Thursday, a fire at a textile mill killed at least 54 workers and wounded dozens in southeastern Chittagong city, 215km southeast of Dhaka.