Two people were killed in a reported gunfight with the detectives at Khilkhet in capital Dhaka early Monday.
Identities of the deceased could not be known immediately. Police claimed they were snatchers.
The incident took place in Kuratali area, Khilkhet Police Station officer in-charge Md Borhanuddin confirmed.
He said two snatchers were preparing for snatching but seeing police they tried to escape that led a gun battle.
The bodies, however, were sent to Dhaka Medical College Hospital morgue, the OC added.