The closures came after Pakistan said it had shot down two Indian Air Force planes in its airspace over disputed Kashmir. India said its forces shot down a Pakistani fighter jet, but also lost one of its own planes.

The air traffic disruption was affecting routes passing through the region that are popular with Western holidaymakers, with an industry body saying that a huge number of flights to Southeast Asia may have to be diverted.

Pakistan's Civil Aviation Authority and the military said the country's entire airspace had been closed, with a CAA source telling AFP that all airlines had been notified to "suspend their operations in Pakistan until further notice".

Pakistan International Airlines, the country's flag carrier, warned that "flights may be affected due to closure of Pakistan commercial air space".

In India, at least six airports were shut -- Srinagar, Jammu and Leh in Kashmir and Amritsar, Chandigarh and Dehradun, and a vast area of airspace north of New Delhi was closed to civilian flights.

Scores of flights were cancelled and many between Asia and Europe that would normally fly over Kashmir have been diverted, aviation company officials said on condition of anonymity.

The Aviation Authority of India did not respond to requests for comment.

A map of live air traffic in the area by monitoring group Flight Radar showed almost no flights over Pakistan or in a strip of land across the border on the Indian side.

"International flights that transit between Indian and Pakistani airspace now being affected," the group said on Twitter.

"Some flights returning to origin, while others appear to be seeking alternate routing."

A spokesman for the International Air Transport Association, an industry group representing many of the world's airlines, did not immediately have details about all the affected flights.

But he said about 220 flights usually pass through Pakistani airspace each day between Europe and Southeast Asia.

"Alternative routes are available for the flights impacted by the closure of Pakistan airspace," he said.

India and Pakistan's ties have been under intense strain since a February 14 suicide bombing in Indian Kashmir that killed 40 troops.