Muzaffarabad, Pakistan -- Pakistan's air force shot down two Indian warplanes near the two rivals' disputed territory of Kashmir on Wednesday and captured an Indian pilot. The dramatic escalation came only hours after Pakistan said mortar shells fired by Indian troops from across the frontier dividing the two sectors of Kashmir killed six civilians and wounded several others. But Pakistan's leader urged calm and called for dialogue on Wednesday, appearing keen to put the brakes on the snowballing tension between the nuclear armed neighbors.

Pakistan's air force shot down two Indian warplanes after they crossed the boundary between the two of Kashmir on Wednesday and captured an Indian pilot, Pakistani officials said. The dramatic escalation came only hours after Pakistan said mortar shells fired by Indian troops from across the frontier dividing the two sectors of Kashmir killed six civilians and wounded several others. But Pakistan's leader urged calm and called for dialogue on Wednesday, appearing keen to put the brakes on the snowballing tension between the nuclear armed neighbors.

In brief:

On Feb. 14 a suicide attack by a terror group killed 40 Indian soldiers in Indian controlled Kashmir

On Feb. 26 India responded with airstrikes deep in Pakistani territory, purportedly targeting the terror group

On Feb. 27 Pakistani jets dropped bombs on the Indian side. Indian warplanes responded, resulting in a dogfight

Pakistan claims two Indian jets were shot down, one in Pakistani territory and one on India's side of Kashmir. It says two pilots were captured and denies any Pakistani jet was shot down.

Pakistani leader Imran Khan calls for talks to de-escalate the situation, given "the types of weapons India and Pakistan have"

Pakistan says "not pushing" for war

Pakistan's army spokesman Maj. Gen. Asif Ghafoor insisted that "Pakistan is not pushing the environment towards war," and he said the country's military had "deliberately avoided" an escalation in its response to the Indian incursion on Tuesday. He said the strikes carried out by Pakistani planes on Wednesday had targeted open land, not attempted to hit Indian military positions as India has claimed.

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Pakistan's Prime Minister Imran Khan reiterated on Wednesday that his country's military deliberately sought to avoid casualties or damage in its strikes inside India, saying the objective was simply to demonstrate the nation's ability to defend itself.

Khan urged "wisdom" and calm and said his government was willing to work with India to investigate the Feb. 14 suicide bombing which sparked the current escalation of tensions.

"If you want any kind of talks on terrorism, we are ready," Khan said, addressing India directly. "There is miscalculation in every war, and the types of weapons India and Pakistan have, can we afford to miscalculate? Where would we go if we start a war?"

"We should sit down and talk," Khan said.

Indian soldiers and Kashmiri onlookers stand near the remains of an Indian Air Force helicopter after it crashed in Budgam district, on the outskirts of Srinagar on February 27, 2019. AFP/Getty Images

CBS News' Arshad Zargar reported on Wednesday that the border areas between the two countries were tense after the jets came down and the limited exchange of fire over night between forces on both sides. Zargar said fear was mounting in India, with some people taking to social media to urge each other to be alert and ready, and stock up on food and fuel.

In a statement issued early Wednesday morning, U.S. Secretary of State Mike Pompeo defended India's strikes on Tuesday as "counter-terrorism actions" and said he had spoken to his counterpart in Delhi "to emphasize our close security partnership and shared goal of maintaining peace and security in the region."

He said he had also spoken to the Pakistani foreign minister "to underscore the priority of de-escalating current tensions by avoiding military action, and the urgency of Pakistan taking meaningful action against terrorist groups operating on its soil. I expressed to both Ministers that we encourage India and Pakistan to exercise restraint, and avoid escalation at any cost."

Indian news reports said airports in the Indian portion of Kashmir closed for civilian traffic shortly after the air force jet crashed in the area. The Press Trust of India news agency said these airports were located at Srinagar, Jammu and Leh. Indian authorities declined to comment.

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."

Press Trust of India said Indian authorities also closed two airports in northern Punjab state, which borders with Pakistan.

The closure of some Pakistani airspace was throwing a wrinkle into air travels around the world on Wednesday. CBS News transport correspondent Kris Van Cleave said routes that would normally pass over Pakistan were having to reroute. Several flights, including U.S. carriers, diverted to refuel in other destinations to fly around Pakistan.

Captured Indian pilot appears in video

Indian military sources confirmed that one Air Force pilot was captured by Pakistan forces, and identified him as Air Force Wing Commander Abhinandan Varthaman .

Pakistan's Khan said two Indian pilots were in Pakistani custody, "but I am asking India, where do we go from here? We must act responsibly." Pakistani officials later clarified that only one pilot was in custody.

Videos circulating on social media appeared to show the pilot being captured and roughed up by civilians as Pakistani forces take him into custody. Another video shows him being interviewed blindfolded and handcuffed by Pakistani Army troops.

A subsequent video, however, posted by a Twitter account with unclear ownership, showed the man in custody and being questioned but in a much more relaxed atmosphere. He responds, in English, to questions from an interrogator in the video which is clearly aimed at portraying Pakistan's treatment of the prisoner in a positive light.

"I hope you have been treated well with us," an unidentified questioner asks him.

"Yes I have," Varthaman replies, unrestrained and sipping from a cup of tea, adding that he "will not change my story if I go back to my country."

He appears to have a bruise on his face and minor cuts and scrapes elsewhere, but he seems overall to be in good health. It wasn't clear how he sustained the injuries, and it is important to note that he was speaking as a prisoner, not of his own free will.

In the seemingly friendly exchange, Varthaman repeatedly says he has been treated well, and even compliments his captors on the "fantastic" cup of tea he was offered.

Near the end of the video the interrogator asks the pilot about his mission and aircraft, to which Varthaman replies, "I'm sorry, I'm not supposed to tell you this." The unseen questioner does not press for an answer in the video, which runs less than a minute and a half.

India lashed out at Pakistan's handling of the prisoner, with the Foreign Ministry saying in a statement that the country "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 and the Geneva Convention. It was made clear that Pakistan would be well advised to ensure that no harm comes to the Indian defence personnel in its custody. India also expects his immediate and safe return."

Kashmir: A disputed region

Kashmir is split between Pakistan and India and claimed by both in its entirety. Though Pakistani and Indian troops in Kashmir often trade fire, the latest civilian casualties came a day after tensions escalated sharply following a pre-dawn airstrike and incursion by India on Tuesday that New Delhi said targeted a terrorist training camp in northwestern Pakistan.

Residents on both sides of the de-factor 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 Tuesday and continued Wednesday. In New Delhi, Indian officials said Wednesday at least five of their soldiers were wounded in firing by Pakistani troops along the volatile frontier.

Lt. Col. Devender Anand, an Indian army spokesman, said Pakistani soldiers targeted dozens of Indian military positions across the Line of Control throughout the night. An Indian military statement said that "out of anger and frustration," Pakistan "initiated unprovoked ceasefire violation."

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."

In Tuesday's pre-dawn strike by India, Pakistan said Indian warplanes dropped bombs near the Pakistani town of Balakot but there were no casualties.

In New Delhi, India's External Affairs Minister Sushma Swaraj said Wednesday 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 Tuesday was to act decisively against the terrorist infrastructure of Jaish-e-Mohammad group, to pre-empt another terror attack in India.

The tension between Pakistan and India erupted after Jaish-e-Mohammad claimed responsibility for the Feb. 14 suicide bombing of a convoy of India's paramilitary forces in the Indian portion of Kashmir that killed 40 Indian troops.

Pakistan has said it was not involved in the attack and was ready to help New Delhi in the investigations.