The incident took place around 2am near BSF's Anuradhapur camp in India, at Charaldanga village near the border in the district's Gomostapur upazila, said officials at the 43 Border Guard Bangladesh (BGB) battalion.
The deceased were identified as Shahjahan Ali Bhutto, from Begpur village in Radhanagar, and Jobdul Haque, from Charaldanga village in Radhanagar.
Speaking to the Dhaka Tribune, 43 BGB Commander Lt Col Zahid Hossain said the victims, along with six others, went across the border to get cattle from India. As the group went around 200 yards in, a troop of 82 BSF battalion intercepted them and opened fire at them.
While others were able to escape and come back to Bangladesh, Shahjahan and Jobdul were killed on the spot.
Later, a flag meeting between the BGB and the BSF took place around 4pm yesterday at Markatta border area in India, where the BGB vehemently protested the killings, Zahid said.
The dead bodies will be handed over to their families today, he added.