Since the terrorist attack earlier this month, Indian Prime Minister Narendra Modi has been under pressure from his base to respond with force ahead of a parliamentary election due to take place by May.

"That India entered Pakistan's airspace is a clear indication that it is willing to do whatever it takes to keep India safe, which, I suspect, caught Pakistan off-guard," Akhil Bery, analyst for South Asia at political consultancy Eurasia Group, told CNBC on Tuesday.

Dhruva Jaishankar, a fellow in foreign policy studies at Brookings India, said India has faced a series of terrorist attacks since the 1990s from groups and individuals based in Pakistan. The challenge for both sides has always been about how to respond to provocations from its neighbor, especially after each country became a nuclear power.

Jaishankar told CNBC that both countries have tested the limitations of how far they can escalate the conflict before reaching a "nuclear threshold."

To be clear, escalating tensions to the point of nuclear conflict would be catastrophic for both India and Pakistan and would destabilize the entire region — an option unlikely to be taken by either New Delhi or Islamabad.

For his part, Pakistani Prime Minister Imran Khan's sway with the country's influential military is limited. The way Khan handles this week's situation will be a big test of his leadership, according to Moeed Yusuf, associate vice president for the Asia Center at the United States Institute of Peace.

"You have a new leader in Pakistan who (has to) show that he is strong and willing to stand up to India," Yusuf told CNBC. "He must also follow the army's lead and so if the army decides to escalate, he won't be able to say much to them right now."

For Modi, meanwhile, it would be "political suicide" if he walked back on the conflict at this stage — when it may appear to outside observers that India and Pakistan had evenly matched each other's force, Yusuf said.