"So far 13 dead bodies have been recovered," sub-inspector Mohammad Alauddin told AFP, adding that military rescue teams had been called in to help with the search for victims.
The number of missing could not immediately be confirmed but police constable Shakakhawat Hossain told AFP from the scene that dozens could be trapped under the debris.
Witnesses said more than 50 construction workers and vegetable hawkers had gathered near a pond under the bridge at the end of work when three concrete girders of the under-construction flyover crashed on Saturday evening.
"Instantly the whole area was covered by smoke and dust," Syed Mainuddin, a witness, told reporters.
Police and local people rescued at least 15 people from the spot and rushed them to hospital, police said.
Chittagong fire brigade chief Abdul Mannan told AFP each of the girders are about 100 feet (30 metres) long and about seven feet wide.
"We are trying to cut the girders into pieces to see if anyone was trapped underneath. We tried to pull the girders up with cranes but they are too heavy," he said.
Divers from the navy, meanwhile, scoured the pond but until the girders were removed chances of finding more dead bodies were remote, he added.
Armed with sticks and stones, angry crowds attacked the site offices of the construction company after the flyover collapsed, forcing police to fire tear gas and use batons to disperse them, Hossain said.
The mob torched at least half a dozen vehicles and set construction material on fire.
Allegations of corruption were levelled at the flyover construction company in August when another girder had collapsed. But only one rickshawpuller was injured in that incident, police inspector Rajib Das said.
In September the World Bank said it was concerned about corruption in Bangladesh, reiterating that it would not get new funding for a bridge project until a credible probe into corruption around the project was undertaken.
The Washington-based institution said it was not yet prepared to reactivate financing for the $3 billion Padma road and rail bridge which was intended to connect the capital Dhaka to coastal districts.
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