An FIR has been lodged against Border Guard Bangladesh (BGB) by its Indian counterpart Border Security Force (BSF) over the killing one of its jawans earlier this week, a senior police officer said.

A Bangladeshi border guard on Thursday fired from his AK-47 rifle during a 'flag meeting' along the international boundary in West Bengal, killing BSF head constable Vijay Bhan Singh (51) and injuring another jawan, Rajvir Yadav.

A BSF statement said the incident took place in Murshidabad district around 9 am when a force party approached the BGB troops, standing at a "char" or a riverine in the middle of the Padma river, to resolve an issue linked to Indian fishermen.

"Yes, we have received a complaint from the BSF. A case has been registered and investigation is on," Murshidabad Superintendent of Police Mukesh Kumar said.

The BSF officials, too, confirmed that police have lodged an FIR against the BGB.

Refuting claims by the Bangladeshi border force that its patrol team "had to open fire in self-defence", a senior official of the BSF said not a single bullet was fired from the Indian side.

"Although an inquiry has been ordered by the BSF, we still decided to lodge a complaint with the police, in accordance with the norms. The allegation by the BGB that we had fired first is not just absurd but a blatant lie. We didn't fire a single bullet," a senior BSF official said.

Officials had said that the trouble arose when BGB personnel held three Indian fishermen who were allowed by the BSF to fish within the International Border, that runs through the middle of the 3-km-wide Padma river.

The BGB team later freed two fishermen and informed the BSF that the third person has been held by them and that was when the BSF post commander of the 117th battalion, a sub-inspector, took a six-member party on a motor-boat to resolve the issue, they said.

Shortly after, a BGB jawan identified only as Sayed fired from behind, killing Bhan Singh.

A senior BSF officer in Delhi said on Friday that the troops "did not try to forcibly take away the lone fisherman from the custody of Border Guard Bangladesh. They had gone for flag meeting inside Bangladesh territory on getting a call from the BGB."

The officer added that during a telephonic talk between the commanding officers of the two sides, post the incident, the counterpart "did not say that BSF men had either violated the IB or entered inside Bangladesh territory."

Security has been stepped up along the 4,096-km Indo-Bangla border in the wake of Thursday's incident. The lone fisherman, Pranab Mondal, is still in Bangladesh police custody.