India has called for the safe and immediate return of a fighter pilot seized by Pakistan after being shot down during tit-for-tat incursions over Kashmir that have edged the pair closer to war than at any point in the past 20 years.

Its pilot, a wing commander identified as Abhi Nandan, appeared in a bloodied uniform as he gave his name and rank in a video released by the Pakistani armed forces. Asked by his interrogator to say more, he replied: “I am sorry, sir, that’s all I’m supposed to tell you.”

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Delhi said it “strongly objected to Pakistan’s vulgar display of an injured personnel of the Indian air force in violation of all norms of international humanitarian law”.

The external affairs ministry said it had summoned the acting high commissioner of Pakistan, Syed Haider Shah, and lodged a strong protest at the violation of the Indian air space by Pakistan and the targeting of Indian military posts.

India earlier said one of its air force Mig-21 fighter aircraft has been “lost” in an engagement with Pakistani aircraft in the Indian portion of Kashmir and that its pilot was missing. Pakistan earlier said it shot down two Indian planes and captured two pilots, but later retracted that claim.

By Wednesday evening, India’s prime minister, Narendra Modi, had yet to comment publicly on the fighting but was meeting military chiefs at his residence in Delhi.

Meanwhile, Pakistan’s prime minister, Imran Khan, appealed for talks, making reference to both countries’ nuclear arsenals.

Khan said in a televised address after the airstrikes that the time had come for a diplomatic solution to the crisis. “With the weapons you have and the weapons we have, can we afford miscalculation? Shouldn’t we think that if this escalates, what will it lead to?”

Facebook Twitter Pinterest Imran Khan’s televised address. Photograph: Anadolu Agency/Getty Images

The dogfights on Wednesday morning were the first between the two air forces to be publicly acknowledged since 1971, and triggered the closure of every commercial airport in Pakistan and at least eight in India. Pakistan also closed its airspace, forcing international flights to be rerouted.

Footage of the captured pilot, including one video showing him being beaten by a crowd of angry civilians, made the rounds of WhatsApp and social media in India, fuelling popular concern and anger. The pilot said in a video released later by the Pakistani military that its soldiers had “rescued me from the mob”, and he was shown sipping tea.

Maj Gen Asif Ghafoor (@OfficialDGISPR) There is only one pilot under Pakistan Army’s custody. Wing Comd Abhi Nandan is being treated as per norms of military ethics. pic.twitter.com/8IQ5BPhLj2

Srinagar, the Indian-controlled capital of the Kashmir region that both countries claim in full, appeared to be preparing for war. Its army headquarters observed a blackout overnight as Indian jets patrolled over the city. On Wednesday afternoon, a red cross was painted on the roof of its largest hospital, marking out the building as a medical facility from above.

In supermarkets in the Pakistani cities of Lahore and Islamabad, people were stockpiling groceries, while in Khyber Pakhtunkhwa province the leave of all police and health workers was cancelled.

Russia, the US and the UK were among the countries calling for restraint amid fears that the region was trapped in a cycle of escalating attacks.

A Pakistan-based militant group killed 40 Indian paramilitaries in a suicide bombing in Kashmir two weeks ago. Indian jets bombed what they claimed were militant training camps in Pakistan on Tuesday morning in response, triggering Wednesday’s reprisal by Pakistan.

Facebook Twitter Pinterest Workers paint a red cross on the rooftop of a hospital in Srinagar. Photograph: Tauseef Mustafa/AFP/Getty Images

Khan said the latest airstrikes were deployed from inside Pakistan-held territory and deliberately aimed at empty fields to send a message. “It was our plan that there should be no collateral damage, no casualties,” he said in his televised address.

“We just wanted to tell India that we have the capability that if you can come into our country, then we can also go into your country and carry out an operation.”

But India rejected his account of the operation. “[Pakistan] used its air force to target a military installation on the Indian side,” the spokesman for India’s foreign ministry, Raveesh Kumar, told journalists in Delhi.

Islamabad initially said it had captured two Indian pilots, but by Wednesday evening it had retracted the claim. Delhi also claimed to have shot down a Pakistani jet, which it said had crashed on the Pakistani side of the border.

The US has played a mediating role in previous escalations of conflict between the neighbours, but on Wednesday Pakistan’s ambassador in Washington said the Trump administration’s failure to condemn the Indian airstrike had contributed to the tension.

Asad Majeed Khan said the US response was “construed and understood as an endorsement of the Indian position – and that is what emboldened them even more”.

The standoff between the two countries is heightened by India’s looming national elections starting in April. For Pakistan, the driving need is to show its more powerful neighbour that it cannot be pushed around.

Arun Sahgal, a retired Indian army brigadier turned policy analyst, said he believed both countries would walk back from the brink. “The events of today indicate a satisfied Pakistani appetite for retaliation,” the Delhi Policy Group senior fellow said.

“Both countries have lost an aircraft each so there is a degree of equivalence. And from a political perspective, the Indian prime minister [Narendra Modi] has come out looking like a decisive leader. So there is nothing more to achieve.”

But the mechanics of drawing down the conflict were another issue and fraught with their own risks, Sahgal said. “That’s where the international community must play some backchannel diplomacy that pushes the two sides together.”

Facebook Twitter Pinterest Pakistani shopkeepers watch Imran Khan’s televised speech. Photograph: Farooq Naeem/AFP/Getty Images

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Nandan, the first Indian fighter pilot captured by Pakistan since a 1999 war between the countries, said in the video released by the Pakistani military that he was being treated well.

The British foreign secretary, Jeremy Hunt, said he was involved in a round-the-clock effort to prevent the crisis from deepening.

He said: “Neither side wants this to escalate. But because of the historic lack of trust between the two countries, it’s a very volatile situation. You don’t have just the governments, but you have public opinion in both countries that is very inflamed. We are urging [both Pakistan and India] to show restraint to stop this situation from deteriorating.”