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Police said they were investigating whether the tiger cubs were poached from the Sundarbans, the world's largest mangrove forest, which has a significant population of endangered Bengal tigers.
But they had no idea where the lion cubs could have come from.
Police acting on a tip-off found the animals in wodden boxes in a car in the western city of Jessore, district police chief Anisur Rahman told AFP.
"We detained two people in this connection. They are animal smugglers who were delivering the cubs to a man at Sharsha," Rahman said, referring to a town on the Indian border.
"We suspect they were being brought here to be smuggled to India," he said.
Bangladesh brought in new laws in 2010 to protect wildlife, but poaching remains rampant.
In 2012, the country's elite police rescued three Bengal tiger cubs after a raid in the capital.
The tiger population in the 10,000 square-kilometre Sunderbans forest dropped to just over 100 in 2015 from an estimated 440 a decade earlier.
The rescue comes just months after Bangladesh police declared victory over crime in the Sundarbans, crediting a gun buyback scheme.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)