An especially volatile aspect of the confrontation was Pakistan’s capture of an Indian fighter pilot. Pakistani military officials posted a photo of him on Twitter sitting in a room, and they said he was being treated “per norms of military ethics.”

But Pakistani television showed a video of the pilot, blindfolded and apparently with blood on his face. India’s Foreign Ministry said it “strongly objected to Pakistan’s vulgar display of an injured personnel” and expected “his immediate and safe return.”

While experts warned that the clash could easily escalate out of control, Pakistani Prime Minister Imran Khan told his nation Wednesday that he wanted to avoid war with India, saying, “Let’s settle this with talks.” There was no public statement, however, by Indian Prime Minister Narendra Modi.

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“Our action was only intended to convey that if you can come into our country, we can do the same,” Khan said, referring to airstrikes by India on Tuesday and Pakistan’s response on Wednesday. Addressing India, he said, “With the weapons you have and the weapons we have, can we really afford a miscalculation?”

The two days of tit-for-tat airstrikes and Wednesday’s aerial dogfight, the first since 1971, were triggered by a Feb. 14 terrorist bombing in Indian-controlled Kashmir that killed 40 Indian security personnel. The bombing, claimed by a Pakistan-based militant group called Jaish-e-Muhammad, was the deadliest single attack in 30 years of protests and conflict over the disputed Himalayan region, which is claimed in its entirety by both nations.

Indian and Pakistani officials gave conflicting accounts of the events. India claimed it had bombed a militant camp inside Pakistan on Tuesday, killing scores, but Pakistan said the bombs had fallen on an uninhabited forested area. Pakistan also denied India’s claims that a Pakistani F-16 fighter jet was shot down.

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The clash drew expressions of alarm from foreign governments and regional analysts, who noted that India and Pakistan have previously fought three conventional wars, two of them over Kashmir. They also engaged in a brief high-altitude fight in the Kargil mountains of Kashmir in 1999, shortly after both countries tested nuclear weapons.

Moeed Yusuf, a Pakistan expert at the U.S. Institute of Peace in Washington, said he feared the conflict could escalate dangerously, in large part because neither Khan, who has been in office only a few months, nor Modi, who is seeking reelection this spring, may be able to back down without losing domestic political stature.

Pakistan’s retaliatory strike punctured a triumphal moment for Modi. After India conducted its operation Tuesday against what it said was a terrorist training camp in Pakistan, members of Modi’s ruling Bharatiya Janata Party celebrated. Amit Shah, the party’s president, wrote on Twitter that the strike was a testament to Modi’s “strong and decisive leadership.”

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By Wednesday, the mood in India had shifted to focus on the fate of its captured pilot, whom Indian media outlets identified as Wing Cmdr. Abhinandan Varthaman. Indian officials said his video while blindfolded violated the Geneva Conventions on the treatment of war prisoners.

In Pakistan, despite official claims about wanting to avoid escalation, a mood of belligerent triumph spread across news stations and online Wednesday. War songs were played, commentators praised the military, and shouts of “God is greatest” could be heard. Images of a burning Indian fighter jet were broadcast repeatedly.

Some Pakistani commentators, however, expressed concern that the situation could rapidly spiral out of control. Imad Zafar, a columnist writing in the online Pakistan Express Tribune, said the Indian attack was a “trap” set by Modi that Pakistan should avoid. “A war between two ­nuclear-armed states can only bring destruction on both sides,” he wrote, calling for dialogue. “. . . We don’t want war, India. Neither should you.”

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Some experts said the tit-for-tat strikes of the past two days might help de-escalate tensions. India has “talked up the strike on the terror camp,” while Pakistan has “captured an Indian pilot and shot down an Indian fighter jet,” said Ajai Shukla, a defense analyst and former army officer in Delhi. “Both sides have something they can hold on to.”

But other observers, including Yusuf, said intervention by foreign powers, including the United States, might be the only way to restore calm. “What started as mere posturing is now a real near-war crisis that can easily spill into real combat,” Yusuf said.

In previous moments of high tension between India and Pakistan, such as the Kargil conflict, the United States played a key role in defusing the situation.

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Acting defense secretary Patrick Shanahan, one of the few national security officials remaining in Washington as President Trump and others are in Hanoi for the summit meeting with North Korean leader Kim Jong Un, has been “focused on de-escalating tensions and urging both of the nations to avoid further military action,” according to a Pentagon statement Wednesday.

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The State Department, in a statement Wednesday, called on India and Pakistan “to cease all cross-border military activity and for a return to stability.” The department also urged Pakistan “to deny terrorists safe haven and block their access to funds.”

Pakistani officials said they have appealed to the United States to become more involved in the crisis, perhaps sending a high-level official to shuttle between the two capitals, and they bemoaned the fact that Washington appears distracted with multiple other crises.

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In a statement issued Tuesday, Secretary of State Mike Pompeo called on both countries to “exercise restraint, and avoid escalation at any cost.” Asad Majeed Khan, Pakistan’s ambassador to the United States, told reporters in a meeting Wednesday that the Trump administration’s failure to condemn India’s initial airstrike in Pakistan had “emboldened them even more.”

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Other countries expressed concern and called on both sides to reduce hostilities.

British Foreign Secretary Jeremy Hunt said that he was “very concerned” about the rising tensions and that he had spoken with his Indian and Pakistani counterparts about it. “Neither side wants to see this escalate further, but this is going to take really critical restraint in the days ahead,” he said. Russia’s Foreign Ministry “expressed hope for the de-escalation of the situation.”

Khan said his government had offered to help investigate the Feb. 14 bombing. Pakistan has denied any links with the attackers, but it has long publicly supported those it calls Kashmiri “freedom fighters” and condemned Indian brutality against protesters. The Indian and Pakistani portions of Kashmir are divided by a militarized “Line of Control.”

Pakistan’s Foreign Ministry said its retaliatory airstrikes were aimed at “nonmilitary targets” to avoid human loss and damage. It said Pakistan has “no intention of escalation, but we are fully prepared to do so if forced.”

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India confirmed that one MiG-21 fighter jet was shot down in an “aerial engagement” with Pakistani forces on Wednesday morning.

Pakistani officials also claimed Wednesday afternoon that India had committed “unprovoked cease-fire violations” along the Line of Control on Tuesday, resulting in the deaths of four civilians, three of them women. A Foreign Ministry statement named the four individuals but did not say where or how they died. It called the alleged targeting of civilian areas “deplorable” and said such cease-fire violations could lead to a “strategic miscalculation.”

As tensions mounted Wednesday, commercial flights were suspended across Pakistan and a swath of northwestern India. For most of the day, flight-tracking websites showed no commercial flights in the air in Pakistan

and none in five regions across the border, including Indian-controlled Kashmir. India’s Civil Aviation Authority later lifted restrictions on flights.

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In Indian-controlled Kashmir, residents braced for the worst. Vikas Bhasin, 61, a shopkeeper in the Poonch region near the Line of Control, said that around 10 a.m., he saw fighter jets that he believed were Pakistani aircraft streaking through the sky. After they passed overhead, Bhasin said, police drove through the area and announced on loudspeakers that there was no need to panic.

In Srinagar, the largest city in Indian-administered Kashmir, residents have been on edge ever since the Feb. 14 attack. Over the weekend, there were reports of residents hoarding fuel and groceries. The closure of the Srinagar airport for much of Wednesday was “serious and unsettling,” said Manzoor Ahmad Bhat, 50. “Things seem to be collapsing.”