More than 90 staff were on the site in the port town of Mongla when the structure started to cave during the afternoon, trapping scores under a rubble of newly mixed concrete and steel, they said.
Soldiers and emergency personnel used two massive cranes and steel cutters to clear some debris, rescuing about a dozen people, government administrator chief Shah Alam Sarder told AFP.
"The death toll is seven and the number of injured is 53 including at least six whose conditions are critical," he added.
It was unclear how many people were still trapped under the rubble of the factory warehouse.
Local police chief Jahedur Rahman told AFP that up to 10 people remained unaccounted for, but fire service director Sheikh Mizanur Rahman said it was nearer 40.
"We've cleared a third of the debris and hope to complete the job by Friday morning," the chief told AFP, adding that no bodies could be seen under the wreckage and no faint cries for help could be heard.
"Still we have to dig carefully as there is still a chance that some people may still be alive," he added.
Injured worker Masud Kazi told the local Daily Star newspaper that they were pouring concrete on the roof when it started collapsing.
"Suddenly, everything broke down," he said, adding that poor scaffolding could have caused the accident.
"I heard a loud noise and saw the roof caving in through the middle," another survivor told private television station Jamuna. Local police chief Rahman said several people were seriously injured after jumping from the collapsing roof.
"Most of the workers who were on the ground floor were mostly able to escape unhurt," he added.
Rahman said the cement factory was owned by Sena Kalyan Sangstha, a company run by the Bangladesh Army. The building contractor was a Chinese firm called China National Building Material (CNBM).
Buildings frequently collapse in Bangladesh owing largely to widespread use of shoddy building materials and a failure to abide by proper engineering and construction rules.
In April 2013 a nine-storey garment factory complex collapsed just outside the capital Dhaka leaving at least 1,138 people dead.
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