The deceased are Mojid, of Matlab Uttar Upazila and Habu, of Lakshmipur district.
Matlab Uttar OC Alamgir Hossain said: “Acting on a tip-off, we conducted a drive in the area around 3:30am on Wednesday.
“Sensing our presence, the robbers opened fire targeting us.”
In retaliation, police fired back that left the two robbers dead. Three policemen were also injured in the incident.
The OC said: “Mojid is accused in eight cases while Habu faces four cases.”