Pakistan's state media Wednesday published a video showing an Indian fighter pilot who was captured after his jet was shot down when it entered Pakistani airspace in Kashmir.

Two Pakistani security sources told AFP the video was authentic.

It shows a blindfolded man in an Indian Air Force uniform, his face bloodied, with his hands tied behind him, as a soldier interrogates him. 

He gives his name, rank and serial number and when pressed for further information says, "I am not supposed to tell you that."

In a photograph, which has also been confirmed by security sources, the pilot can be seen flanked by Pakistani military personnel.

The Pakistani military released a second video hours later showing the same man sitting in a room in an unknown location drinking a cup of tea.

"The tea is fantastic," he says in English, adding that he is married and being treated well, but politely declining to answer further questions.

Both Pakistan and India Wednesday claimed they had shot down each others warplanes, in a dramatic escalation of the dangerous confrontation between the nuclear-armed rivals.

Islamabad said it downed two Indian jets in its airspace and captured two pilots, but insisted it does not "want to go towards war" with its neighbour.

Pakistani military spokesman Major General Asif Ghafoor said one of the downed Indian planes had fallen in Pakistani-held Kashmir, while the other came down on the Indian side of the heavily militarised de facto border dividing the territory. 

He said one of the captured pilots was in custody and the other was in hospital.

The Indian foreign ministry said only one of its planes had been shot down. 

"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," said Indian foreign ministry spokesman Rajeesh Kumar.

He also said a Pakistani jet had been shot down by Indian forces. Pakistan denied that any of its planes have been downed.