Pakistan's prime minister Imran Khan has extended an offer to Indian prime minister Nerendra Modi for talks to de-escalate rising tensions between the two nuclear-armed neighbours.
Mr Khan said war benefits neither nation and that he hopes "better sense can prevail".
In a televised address to the nation, Mr Khan said Pakistan is "ready to cooperate" and added: "Let's sit together to talk to find a solution."
Former cricketer Mr Khan again promised to cooperate with India to find the perpetrators behind a February suicide attack in Indian-controlled Kashmir that killed more than 40 Indian troops.
The Pakistan-based Jaish-e-Mohammad group claimed responsibility and the suicide bomber was from Indian-ruled Kashmir.
India has long accused Pakistan of harbouring anti-Indian militants, a claim Pakistan denies.
India's Ministry of External Affairs spokesperson has confirmed that one Pakistan fighter aircraft was shot down, one Indian MiG-21 jet 'was lost' and an Indian pilot is missing in action.
Pakistan’s air force said it has shot down two Indian warplanes after they crossed the boundary between the two nuclear-armed rivals in the disputed territory of Kashmir, with two Indian pilots being captured.
The civil aviation authority in Pakistan later shut all airspace in the country to commercial flights.
Pakistan’s army spokesman Major General Asif Ghafoor said Pakistani troops on the ground captured the pilots. He added that one of the downed planes crashed in Pakistan’s part of Kashmir, while the other went down in Indian-controlled section of the Himalayan region.
The injured pilot is being treated at a military hospital. Maj Gen Ghafoor said the pilots are being treated well, but made no mention of them being returned to India.
He struck a conciliatory tone, saying: “We have no intention of escalation, but are fully prepared to do so if forced into that paradigm.”
Earlier, senior Indian police officer Munir Ahmed Khan said an Indian air force plane crashed in Indian-controlled sector of Kashmir and that it was not immediately known if there were casualties.
Another police officer, SP Pani, said firefighters were at the site in Budgam area in Indian-controlled Kashmir where the Indian warplane crashed. Eyewitnesses said soldiers fired into the air to keep residents away from the crash site.
Indian administrator Baseer Khan confirmed that the airport in Srinagar, the main city in Indian-controlled Kashmir, was closed and said it was a “temporary and precautionary measure”. The Press Trust of India said two airports in northern Punjab state, which borders Pakistan, were also closed.
Meanwhile, the foreign ministry in Islamabad said the country’s air force was carrying out air strikes from within Pakistani airspace across the disputed Kashmir boundary, but that this was not in “retaliation to continued Indian belligerence”.
Maj Gen Ghafoor said the strikes were aimed at “avoiding human loss and collateral damage”.
According to local Pakistani police official Mohammad Altaf, the six fatalities in the Indian shelling earlier on Wednesday included children. The shells hit the village of Kotli in Pakistan’s section of Kashmir.
In Tuesday’s strike by India, Pakistan had said that Indian warplanes dropped bombs near the Pakistani town of Balakot, but there were no casualties.
Residents on both sides of the de facto frontier, the so-called Line of Control, said there were exchanges of fire between the two sides through the night. In Pakistan’s part of Kashmir, hundreds of villagers fled border towns.
The situation was no different in villages along the Line of Control in Indian-controlled Kashmir, where residents were moving to safer places following the intense exchange of fire, which began on Tuesday and continued on Wednesday. In New Delhi, Indian officials said at least five of their soldiers were wounded in firing by Pakistani troops along the volatile frontier.
The statement said Indian troops “retaliated for effect” and claimed to have destroyed five Pakistani posts. It accused Pakistani soldiers of firing mortars and missiles “from civilian houses, using villagers as human shields”.
Pakistani prime minister Imran Khan is expected to convene the National Command Authority to discuss Islamabad’s response to the incursions by Indian warplanes.
On Wednesday, Pakistan’s foreign minister Shah Mahmood Qureshi told state-run Pakistan Television he was in touch with his counterparts across the world about the “Indian aggression”, adding that New Delhi had endangered peace in the region by Tuesday’s air strike on Pakistan.
In New Delhi, India’s external affairs minister Sushma Swaraj said her country does not wish to see further escalation of the situation with Pakistan and that it will continue to act with responsibility and restraint.
She said the limited objective of India’s pre-emptive strike inside Pakistan on a terrorist training camp was to act decisively against the terrorist infrastructure of the Jaish-e-Mohammad group.
The latest wave of tensions between Pakistan and India first erupted after Jaish-e-Mohammad claimed responsibility for a suicide bombing of a convoy of India’s paramilitary forces in the Indian portion of Kashmir which killed 40 Indian troops on February 14.
Pakistan said it was not involved in the attack and was ready to help New Delhi in its investigations.