The Pakistani fighter jet was hit as it took part in an operation "to target military installations on the Indian side", spokesman Rajeesh Kumar told a briefing, adding that the attack was "foiled".

The action marked a new escalation a day after Indian jets hit a militant camp inside Pakistan territory.

"The Pakistani aircraft was seen by ground forces falling from the sky on the Pakistan side," Kumar added.

"In this engagement, we have unfortunately lost one Mig-21. The pilot is missing in action. Pakistan has claimed that he is in their custody."

The spokesman did not say where the battles took place, but media reports said Pakistan jets entered Indian Kashmir airspace early Wednesday. Many civilian airports in the region were closed for several hours after.

Pakistan had vowed to retaliate for an attack Tuesday at Balakot which India said was to hit a Jaish-e-Mohammed militant camp.

The group claimed responsibility for a February 14 suicide attack in Indian Kashmir in which 40 Indian paramilitaries were killed.

"Pakistan has responded this morning by using its air force to target military installations on the Indian side," said Kumar.

He said the Pakistani jet was shot down in an "aerial engagement" by an MiG 21 Bison.

Pakistan said earlier it had shot down two Indian planes.