Pakistan 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.
India confirmed the loss of one of its planes and said it had shot down a Pakistani fighter jet, in a conflict played out over the skies of the disputed Himalayan region of Kashmir.
In a sign of the deepening crisis, Pakistan closed its airspace "until further notice". At least six airports were shuttered in India, and a vast area of airspace north of New Delhi was closed to civilian flights.
A Pakistani military spokesman said that 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.
"We do not want escalation, we do not want to go towards war," Major General Asif Ghafoor told a press conference, calling for talks with New Delhi.
One of the captured pilots was in custody and the other was in hospital, he said.
Ghafoor said the jets had been shot down after Pakistani planes earlier flew across the Line of Control, the de facto border in Kashmir, to the Indian side in a show of strength, hitting non-military targets including supply depots.
Afterwards, he said, the two Indian planes crossed the LoC into Pakistani airspace.
"The Pakistan Air Force was ready, they took them on, there was an engagement. As a result both the Indian planes were shot down and the wreckage of one fell on our side while the wreckage of the other fell on their side," he said.
He denied initial reports that a Pakistan plane had been shot down, saying accounts an F-16 had been lost were incorrect as none were used in the action.
- 'Unfortunate loss' -
Later, Indian foreign ministry spokesman Rajeesh Kumar announced that a Pakistan jet was hit as it took part in an operation "to target military installations on the Indian side".
"The Pakistani aircraft was seen by ground forces falling from the sky on the Pakistan side," he told a briefing.
"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."
In a separate incident, a helicopter crashed and exploded into flames outside the main city of Srinagar in Indian-administered Kashmir, killing three people, officials said, adding they were investigating the cause.
The incidents are the latest in a dangerous sequence of events between the two countries, whose ties have been under intense strain since a February 14 suicide bombing in Indian Kashmir that killed 40 troops.
New Delhi had promised to act, and on Tuesday its warplanes flew into Pakistani airspace and struck what it said was a camp of Jaish-e-Mohammed (JeM), the militant group that claimed the Kashmir bombing.
It was India's first air strike on Pakistani soil since the neighbours fought a war in 1971 -- when neither had nuclear weapons.
Islamabad, while denying the Indian strike caused any major damage or casualties, quickly vowed to retaliate, fuelling fears of a disastrous confrontation in South Asia.
- Appeal against 'escalation' -
Earlier Wednesday, the Indian foreign minister sought to ease the situation by downplaying Tuesday's strike, repeating Indian claims that it had been a pre-emptive attack on JeM as the group planned further assaults.
"India does not wish to see further escalation of this situation. India will continue to act with responsibility and restraint," Sushma Swaraj said during talks in China with her counterparts from Beijing and Moscow.
The US, along with China and the European Union, have called for cooler heads to prevail.
"We encourage India and Pakistan to exercise restraint, and avoid escalation at any cost," US Secretary of State Mike Pompeo said after speaking with his counterparts from both countries.
China Wednesday again urged the two sides to "exercise restraint" and seek dialogue.
- Crisis for Khan -
The confrontation represents the first major foreign policy crisis for Pakistani Prime Minister Imran Khan, who is believed to be close to the powerful military and who came to power last year vowing to seek dialogue with New Delhi.
Pakistan has denied involvement in the Kashmir bombing on February 14.
While India has consistently accused its neighbour of supporting extremist groups, Pakistan has equally vehemently denied any role in attacks in India and its only Muslim-majority state, Kashmir.
The Himalayan region has been divided between India and Pakistan since independence in 1947. They have fought two of their three wars over the territory.
Previously, the US and other members of the international community have acted to defuse tensions.
"If I were Washington, I'd be in overdrive making phone calls and signalling that it wants tensions to be de-escalated now," said Moeed Yusuf, an expert at the US Institute of Peace in Washington.
"The risks of letting this play out are too great."