One of the deceased was identified as 30-year-old Sohel.
Tajul Islam, officer-in-charge of Abhaynagar Police Station, said a gang of thieves came to the village around 4am and stole three cows from the house of one Khorshed Ali.
Residents of the house shouted for help when they realised that there were thieves.
Villagers learned about the theft attempt after it was announced on a loudspeaker of a nearby mosque. They came out of their houses and chased the thieves just after 4am, the OC said.
Three of the thieves were caught at a rail crossing in Majumdarpara.
Two of them died on the spot while being beaten by the villagers. Another suspected thief, injured in the mob beating, died when he was being taken to the hospital.
Police recovered the bodies and seized a pickup which was brought by the suspected thieves.