New Delhi's appeal to Dhaka came a day after Bangladesh Rifles (BDR) resorted to 'unprovoked firing' on Indian villagers under Meghalaya sector.
Border Security Force (BSF) officials had also held a telephonic conversation with the BDR wherein they protested against yesterday's firing incident and asked them to maintain status quo.
A primary school teacher was injured in her right leg when the BDR bullet hit her.
Meghalaya Chief Minister Mukul M Sangma, who is on his way to Shillong from New Delhi, said he has taken has taken up the matter with Union Home Minister P Chidambaram.
''I have asked the Home Minister to take appropriate action (BDR firing) on an urgent basis, as the attack is perceived by us as a threat on our local people residing in those areas,'' Dr Sangma told UNI over phone.
He said the Centre must take urgent steps to ensure security to the people residing along the Indo-Bangla border.
Inspector General of BSF (Assam-Meghalaya) frontier RC Saxena said the situation in the Jaintia Hills sector was tense in the border areas.