The deceased were identified as Dhanesh Sarkar alias Sukumar Sarkar, 38, son of Mantu Sarkar of Gaibandha Sadar upazila, and Afzal Hossain, 55, son of Rajab Ali of Natore’s Singra upazila.
Police said Afzal was wanted in 20 criminal cases and Dhanesh in 11 cases.
Sanatan Chakrabarty, additional superintendent of Bogura police (media cell), said they sent a team to the spot around 1am after learning about the gunfight.
Gaziur Rahman, additional superintendent of Sherpur Circle, and Humayun Kabir, officer-in-charge of Sherpur Police Station, led the team.
Police found Dhanesh and Afzal with gunshot wounds and took them to Shaheed Ziaur Rahman Medical College Hospital where doctors pronounced them dead.
A shutter gun, a pipe gun, and two bullets were recovered from the spot.