The incident occurred at Beldanga locality under Tilason border outpost when a group of rustlers were smuggling cattle across the international border amid dense fog last night.
The BSF personnel chased the smugglers who attacked the border guards with bombs injuring a jawan, identified as Yogesh, the sources said.
The guards then opened fire killing two smugglers on the Bangladesh side of the border. The two were identified as Bangladeshis, the sources said.
The animals, in the meantime, had been chased inside the Bangladesh territory and could not be retrieved.