Indian Prime Minister Narendra Modi's may have room to ease tensions with arch rival Pakistan, if his counterpart offered certain concessions such as the return of a captured pilot, a political analyst said Thursday. Tensions between the two nuclear powers spiraled this week, after military planes from both sides carried out tit-for-tat air strikes in each other's territories, and as their troops traded fire along their de facto border in Kashmir. New Delhi and Islamabad also claimed to have brought down each other's military jets. Pakistan also said an Indian pilot was taken into custody on Wednesday. Later, a video surfaced that appeared to show the captured pilot who was attacked by a mob and then paraded around by the Pakistani army. India's external affairs ministry said in a statement it "strongly objected to Pakistan's vulgar display of an injured personnel of the Indian Air Force" and accused Islamabad of violating the Geneva Convention, which calls for humane treatment of prisoners-of-war. On Thursday morning, reports said the countries briefly exchanged fire in a district in Indian-occupied Kashmir. Pakistan has closed its airspace, which forced commercial airlines to reroute.

Indian government and military forces attend to the scene of a crashed Indian Air Force aircraft on February 27, 2019 in Budgam west of Srinagar, the summer capital of Indian administered Kashmir, India. Yawar Nazir | Getty Images

This week's escalation was triggered after Jaish-e-Mohammed (JeM), listed by the U.S. as a terrorist organization, claimed responsibility for an attack in India-controlled Kashmir on Feb. 14 that killed more than 40 Indian security officers. For its part, India said it carried out incursions inside Pakistani territory against a JeM militant camp that it claimed was planning terrorism attacks against the country. Pakistan, on the other hand, said its actions a day later were to demonstrate its ability to respond to potential acts of aggression from India.

I think what we have to watch here, carefully, is what they do with the pilot who has been captured. Tanvi Madan director of the India Project at Brookings Institution

India and Pakistan have fought three wars since independence from British colonial rule in 1947 and two of them were over the disputed region of Kashmir. Modi, who is heading into a parliamentary election this year in order to stay on as prime minister, is now under pressure to respond in a way that would appeal to his base but also prevent the outbreak of war. He addressed his Bharatiya Janata Party on Thursday through a video conference and said India will stand united with its soldiers to ensure the country remains strong. "When the enemy supports terror and carries out activity against India, it is with the intent that India's progress gets stalled," he said, according to a translation by NDTV.

Pilot's fate

The fate of the Indian pilot underpinned the future of the contentious relationship between South Asian rivals, Tanvi Madan, director of the India Project at Brookings Institution, told CNBC's "Squawk Box." "I think what we have to watch here, carefully, is what they do with the pilot who has been captured," she said. "What could really diffuse the situation is, for example, Pakistan offering to ... return the pilot to India without pre-conditions and say 'This is a sign of good faith, a confidence building measure.'" Alternatively, Pakistan could take some type of action against the JeM terrorist group, "which operates from its soil, and it has a fair amount of infrastructure there that both the U.S. and India have pointed to," she said. Policy experts have pointed out that the ball is in India's court to decide how it would respond.

Neither wants war

Political scientists anticipate that further military escalation from India in the coming days would be met with retaliation from Pakistan. While neither country wants to go into a full-blown war, both do not want to be the first to back down from the confrontation, they said. "So now the question is: Does India want to give a further military response, possibly through further air strikes, or does India then return to a more traditional format?" Faisel Pervaiz, South Asia analyst at consultancy Stratfor, told CNBC's "Street Signs."

The traditional format, according to Pervaiz, is for India to keep up the pressure on Pakistan along the so-called Line of Control — the de facto military border between Indian- and Pakistani-controlled parts of Jammu and Kashmir — and embark on a diplomatic campaign to isolate Islamabad globally. Consensus among many policy experts is that neither India nor Pakistan wants to further escalate their confrontation. Their predicament, however, is that on one hand, each country wants to demonstrate strength and firmness against any form of aggression by its neighbor — yet both also clearly want to calm things down, Pervaiz said. Pakistani Prime Minister Imran Khan on Wednesday called for talks with India and said he hoped "better sense" would prevail to reduce the tension between the nuclear-armed neighbors. On Thursday, Khan said the pilot would be released on Friday as a peace gesture.

Political implications

Modi is "operating in a very narrow and restricted domestic political space" ahead of a tough re-election campaign, Pervaiz said. Already, opposition parties in India have accused Modi of "blatant politicization" of the armed forces. In a statement on Wednesday on behalf of 21 political parties, the leader of the Indian National Congress, Rahul Gandhi, condemned Pakistan's response but also said, "National security must transcend narrow political considerations."

Prime Minister of India Narendra Modi waves his hand after casting his vote during the presidential election, at the Parliament House on July 17, 2017 in New Delhi, India. Sonu Mehta | Hindustan Times | Getty Images

Still, a diplomatic, non-military response from New Delhi could potentially alienate Modi from his base after he positioned himself as a politician willing to do whatever it takes to protect India. After Tuesday's air strike by the Indian air force, the prime minister said at a rally in Rajasthan that the country is in "safe hands" as his supporters cheered. His party has lauded him for his "strong and decisive leadership," which puts him in a difficult position to open negotiations with Pakistan until the captured Indian pilot is returned safely, according to Akhil Bery, South Asia analyst at Eurasia Group.

Economic impact