Indian border officials have admitted killing three Bangladeshi nationals who they say were trying to enter Indian territory illegally.
Bangladesh, however, says that Indian troops opened fire without provocation on workers who had been lifting sand from the Shalda river on the border.
India is constructing a barbed wire fence along the border to keep out what it describes as illegal immigrants.
The two countries have had several border skirmishes in recent months.
A spokesman for the Indian Border Security Force (BSF) told the BBC that nearly 100 Bangladeshi nationals had been found trying to enter Indian territory at Kamthana in the north-eastern state of Tripura.
SK Mitra said that the Bangladeshi nationals had opened fire on BSF troops when they were challenged.
Indian troops had fired back killing two Bangladeshi nationals.
However, Bangladeshi officials deny that those killed were within Indian territory.
Colonel Jahangir Alam, local commander of the Bangladesh Rifles (BDR) said that BSF troops opened fire, without provocation, on workers lifting sand from the Shalda river.
He accused BSF troops of coming into Bangladeshi territory to forcibly remove two of the injured men.
India is trying to construct a barbed wire fence along the border
In a separate incident, BSF spokesman SK Mitra said that the BSF had opened fire on three Bangladeshi nationals who had been found cutting the barbed wire fence at Kukrada, in the Indian state of West Bengal.
One man died in this incident, he said.
BDR officials said that the dead body of a Bangladeshi had been seen hanging from the barbed wire fence in the early hours of Tuesday morning.
Bangladesh and India enjoy generally friendly relations but tensions have increased since India began fencing off its border to keep out what it describes as illegal immigrants and "cross-border insurgents".
Several skirmishes have been reported between the two border forces during the past year.