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Afrozul Hoque Tutul, Additional Superintendent of Police of Cox's Bazar district, told Xinhua news agency in the evening that 14 bodies had been recovered.
The accident also left an unknown number of people missing, the police official said.
Law enforcers rushed to recover the bodies floating in the Bay of Bengal near Inani sea beach area of Cox's Bazar district, 292 km southeast of capital Dhaka, he said.
He said there was no information about how many people from the sunken boat managed to swim ashore after it capsized.
The official said the death toll was likely to rise as search operation for the missing was underway.