Pakistan's Prime Minister Imran Khan has called for talks with India after both sides said they had shot down each other's warplanes, a dramatic escalation of the confrontation between the nuclear-armed rivals.

"I once again invite India to come to the negotiating table," Mr Khan, who has called for dialogue with New Delhi in the past, said in a televised statement.

"Better sense should prevail," he added, before alluding to the nuclear arsenal of both South Asian countries and asking: "If escalation begins from here, where will it go?"

Earlier, Pakistan carried out airstrikes and shot down two Indian jets, Pakistani officials said, a day after Indian warplanes struck inside Pakistan for the first time since a war in 1971.

Pakistan closed its airspace after the incident.

The Civil Aviation Authority (CAA) tweeted that it "has officially closed its airspace until further notice", while a Pakistani military spokesman said the decision had been taken "due to the environment".

A CAA source told AFP that all airlines had been notified.

Ground forces have exchanged fire in more than a dozen locations in recent days.

Tensions have been elevated since a suicide car bombing by Pakistan-based militants in Indian-controlled Kashmir killed at least 40 Indian paramilitary police on 14 February.

The risk of conflict rose dramatically yesterday when India launched an airstrike on what it said was a militant training base.

The attack targeted the Jaish-e-Mohammed (JeM), the group that claimed credit for the suicide attack.

India said a large number of JeM fighters had been killed, but Pakistani officials said the strike was a failure and inflicted no casualties.

Indian air force planes strayed into Pakistani airspace today after Pakistan carried out airstrikes in Indian-occupied Kashmir, said spokesman for the Pakistan armed forces.

One of the aircraft crashed on India's side of Kashmir, while the second came down in Pakistani-held territory and its pilot was captured, he added.

In a statement, Pakistan's foreign ministry said it had hit a "non-military" target inside Indian-controlled Kashmir, but that it had avoided human loss and collateral damage.

"If India is striking at so called terrorist backers without a shred of evidence, we also retain reciprocal rights to retaliate against elements that enjoy Indian patronage while carrying out acts of terror in Pakistan," the statement said.

Police officials in Indian-occupied Kashmir said that two Indian pilots and a civilian had died after an Indian air force plane crashed in Kashmir, but did not confirm if the plane had been shot down by Pakistani forces.

Indian officials said three Pakistani jets had also entered Indian airspace, before being intercepted and forced to turned back.

The Indian air force has ordered Kashmir's main airport in Srinagar along with at least three others in neighbouring states to close because of the two incidents, an official said.