The deceased were identified as Suruj Mia, 35, son of Osman Ali of East Amjhol village, and one Suruj Ali.
Commanding Officer of Lalmonirhat BGB-15 Battalion, Lieutenant Colonel SM Touhidul Islam, said BGB member recovered Suruj Mia’s body in the morning about 50 yards inside Bangladesh territory.
Locals said that BSF had also shot dead Suruj Ali and took away his body.
Lt Col Touhidul said they sent a letter to BSF for a flag meeting to get back the body.
Border killing has been a contentious bilateral issue between the two neighbours who share a porous 4,100 kilometres border.
Delhi had promised to bring down border killings to zero over the years but the BSF, often described as a trigger-happy force, continues to shoot dead Bangladeshis along the border.
Odhikar, a local human rights organisation, said 1,144 Bangladeshis were killed by BSF between 2000 and 2018.
Border killings rose by threefold last year when the BSF killed at least 43 Bangladeshis , according to human rights organisation Ain O Salish Kendra (ASK).