Reports said the Border Security Force and the Bangladesh Rifles exchanged fire at three points --Lalmunirhat and Kurigram on the border with West Bengal's Cooch Behar district and Khagrachhari on the Tripura border.
Bangladeshi officials blamed Indian troops for the deteriorating situation, accusing India of reneging on a 1974 pact which bars defensive construction 150 metres from the border on each side.
India, which does not consider the fencing to be a 'defence work' accused the BDR of trying to stall the fencing by unprovoked firing along West Bengal's Cooch Behar district and in Tripura's Udaipur sector last week.
Officials said the BDR had made repeated attempts over the past 10 days to stop construction of border fencing in South Tripura's Sabroom subdivision bordering the Chittagong Hill Tracts, by firing on construction workers in an attempt to intidimate them.
Following last week's skirmishes, military officials from the two sides held a flag meeting on Monday.
According to the United News of Bangladesh, it was decided that India would stop construction of the fence till a Sector Commander level meeting set for March 17
But since Tuesday, BSF men piled up construction material at the border and tried to start construction along the no man's land Wednesday afternoon in transgression of the truce, it said.
On Wednesday, the BSF opened fire about 3:15 p.m after BDR officials protested attempts to build a fence near the border, and the BDR retaliated, the agency said.
Over 3,000 rounds were exchanged in the first hour, and a Bangladeshi peasant was injured in the crossfire, the agency said. Bangladeshi villagers reportedly fled homes from around the trouble spot and took shelter in Hatibandha sub district headquarters. The BSF had also used mortars, it alleged.
Insisting that the fencing work would continue, Indian officials pointed out that following Home Minister Shivraj Patil's visit to Tripura in January, it was decided that the 150 metre buffer was irrelevant in thickly-populated border areas where markets, schools or government offices existed near the border.