At least 13 people were killed and dozens are feared missing after a flyover under construction collapsed in Bangladesh's southeastern port city of Chittagong, police said on Sunday.

"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.

Hossain said about 20 people were injured, including some during clashes between police and an angry crowd that attacked the site offices of the construction company after the flyover collapse on Saturday evening.

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.