NEW DELHI (AFP) - Prime Minister Narendra Modi called on Indians on Thursday (Feb 28) to "stand as a wall", with anger boiling over Pakistan's capture of a pilot as a crisis escalates between the nuclear-armed rivals.

In his first remarks since India and Pakistan both claimed to have shot down each other's fighter planes near the disputed border of Kashmir, the Prime Minister urged his countrymen to unite, "as the enemy seeks to destabilise India".

"In the face of their objective, every Indian should stand as a wall, as a rock," Mr Modi said.

"The entire country is one today and standing with our soldiers. The world is looking at our collective will and we have faith in our forces' capacity," he said.

"India will live as one. India will work as one. India will grow as one. India will fight as one. India will win as one."

Mr Modi did not mention Pakistan by name during the address to party workers.

But the rival neighbours have been urged by major world powers to exercise restraint after Indian and Pakistani fighter planes fought a brief skirmish on Wednesday morning over the disputed Himalayan territory of Kashmir.

New Delhi said it lost one fighter jet, and a pilot was missing in action. It later confirmed he was in Pakistani custody. India also downed a Pakistani jet, the Foreign Ministry said.

Pakistan claimed to have shot down two Indian jets and denied it lost any aircraft in the dogfight.

Islamabad said its incursion across the heavily militarised border was in response to Indian warplanes bombing Balakot, well inside its territory, on Feb 26.

That attack was the "jaw breaking" response Mr Modi had promised after militants staged a suicide bombing on the Indian side of Kashmir on Feb 14, killing at least 40 paramilitary personnel.

New Delhi blamed the Pakistan-based Jaish-e-Mohammad for the attack, and hit what it called a training camp for the militants in its aerial raid 12 days later.