They had fled across the border to Bangladesh amid heavy fighting between the Myanmar military and rebel insurgents in Rakhine
The shootout took place in Shirkhara area on Monday, said Subrata Kumar Halder, superintendent of Madaripur police.
The man has been identified as Alim Molla, resident of the Kamalapur area in the district.
Police claim Alim was the leader of a motorcycle gang and was named in several cases for robbery.
A gang of DB police conducted an operation in Shirkhara area after receiving information that a group of robbers was preparing for a robbery, Subrata said.
“The robbers opened fire on police and the detective team retaliated. Alim died on the spot.”
A shotgun was recovered from the scene, police said.