India has put its Border Security Force (BSF) on alert at the Bangladesh border as tension is roiling in the region due to an ongoing India-Pakistan conflict over Kashmir.

The BSF has issued an alert and taken all preventive measures at the India-Bangladesh border, reports India's national news agency PTI citing a BSF official.

The measures aim to ensure "miscreants or terror elements" do not cross over taking advantage of the tension at the Indo-Pakistan border, the official said yesterday.

Bangladesh and West Bengal share about 2,216.7 km border, of which a large portion is unfenced.

Patrolling in the riverine border areas of the Sundarbans has also been increased, the BSF official said.

India and Pakistan both said they shot down each other's fighter jets yesterday, with Pakistan capturing an Indian pilot a day after Indian warplanes struck inside Pakistan for the first time since a 1971 war, prompting world powers to urge restraint.

Both countries have ordered air strikes over the last two days, the first time in history that two nuclear-armed powers have done so, while ground forces have exchanged fire in more than a dozen locations.

Tensions have been running high since at least 40 Indian paramilitary police died in a February 14 suicide car bombing by Pakistan-based militants in Indian-controlled Kashmir, but the risk of conflict rose dramatically on Tuesday when India launched an air strike on what it said was a militant training base.