India and Bangladesh have accused each other of cross border shelling.
The two sides regularly exchange fire
Authorities in north-eastern India say two civilians were killed when Bangladeshi forces fired on Indian border positions.
Security official SK Datta said more than 70 shells were fired on Indian posts in Assam state and that two women died when a shell fell on their home.
But Bangladesh says that it was returning fire after India launched about 50 mortar shells into Bangladesh.
India and Bangladesh share a long and porous border and the two sides regularly exchange fire.
Mr Datta said one child was also wounded in the shelling.
Reports from India say Indian soldiers retaliated but casualties, if any, on the Bangladeshi side are not known.
"The firing is still going on .. the situation is tense," an unnamed Indian official was quoted saying by the Reuters news agency.
But Bangladesh border officials say that residents of four villages were forced to flee when the Indian border force "suddenly" started firing across the border.
A military spokesman said that the exchanges began on Wednesday, and around 1,000 rounds were exchanged between then and Thursday morning.
Bangladeshi officials say that the Indians have been claiming an area of land on the border as their own, which led to the recent firing.
Bangladesh and India enjoy generally friendly relations but tensions have increased since India began fencing off its 4,000km (2,500 mile) border to keep out what it describes as illegal immigrants and "cross-border insurgents".
The two countries have had several skirmishes over their border - which is in not properly demarcated - in recent months.