India's Border Security Force - or BSF - says Bangladeshi military helicopters have intruded into Indian airspace on several occasions in the past two days.
Indian troops regularly exchange fire across the border
They said the incidents took place in a frontier region which has witnessed repeated encounters between the two border forces over the past two months.
The head of the Bangladesh border guards has denied the reports.
Bangladeshi officials on Saturday said two farmers had been shot dead by Indian border troops in the south-west.
Long gun battles
The BSF says that the Indian air force has been asked to check on the intrusions and a formal complaint will then be filed.
The BSF's Inspector General for Tripura-Mizoram frontier, Suresh Kumar Dutt, told the BBC's Subir Bhaumik in Calcutta that his troops observed Bangladesh military helicopters flying across the border into Indian territory.
He said the intrusions were reported from Chotakhil, Magrum and Beltoli, all in the southern district of the Indian state of Tripura.
This was the sector where the two border forces fought long gun battles in March this year.
However, Bangladesh has dismissed the allegations out of hand.
The Director General of Bangladesh Rifles (BDR), Major General Jahangir Alam Chowdhury, said his force has only one helicopter, which is being kept with the Bangladesh Army.
"We need several days notice if we want to use the helicopter. It's totally baseless that our helicopter violated the Indian airspace," he told the BBC.
The BDR has for its part accused the BSF of flying helicopters over the tense border, but Mr Dutt said the timings given by the BDR matched commercial flight landings at Agartala airport that is on the border.
Mr Dutt conceded that the BSF has also reinforced their outposts to match additional BDR deployments.
Our correspondent says that the entire Tripura-Bangladesh border has become tense, first after encounters following a border fence India is trying to erect, and then over the killing of Jivan Kumar on 16 April.