Indian Wing Commander Abhinandan was captured when his warplane was shot down on Wednesday.
He also said that an Indian plane had shot down a Pakistani fighter jet, and Indian ground forces observed it falling on the Pakistani side of the LoC.
"They have been going at it and we have been involved in trying to have them stop", Trump said in Hanoi, where he was attending a summit with North Korea's leader.
Meanwhile, US President Donald Trump is hopeful of a resolution to the India-Pakistan crisis.
Speaking to a conference of BJP workers and volunteers, Modi said Thursday that Indians must stand together, and not let what he called the "enemy" slow the nation's progress.
"The world is observing our collective will".
World powers have been watching the situation in Asia unfold with unease and called for de-escalation after a February 14 suicide bombing killed over 40 Indian paramilitary troops in Kashmir in the territory it controls. India again refute the claim, saying only one of their pilots has been captured. In the ensuing dogfight, one Indian aircraft was shot down and its pilot captured. By comparison, the Indian military accounted for 9.1 percent of government spending in 2017. India made it clear to Pakistan that the pilot would not be a "bargaining chip".
"The firing continued in intervals throughout the night".
Virgil van Dijk doubles up after Sadio Mane produce moment of magic
To have that awareness to take the touch and, with your back to play, back-heel it over the keeper, it was unbelievable skill. Liverpool had drawn three of their previous four league games, but never looked like dropping points on Wednesday.
Disinformation campaign by Pakistan Pakistan had carried out heavy ceasefire violations along the border and these are being responded to, he said.
In India, an official from Modi's ruling Bharatiya Janata party predicted the exchange of airstrikes with Pakistan would help his party win more seats in parliamentary elections expected this spring.
The South Asian rivals, divided by the bloody 1947 partition of India, command two powerful militaries armed with nuclear weapons that remain a constant source of concern for global powers.
"The country is in safe hands", he told the cheering crowd.
"Our defence forces are serving gallantly at the border", he told tens of thousands gathered across the country to listen to him in a videoconference from New Delhi. Moscow and New Delhi have long enjoyed close ties that were demonstrated by India's recent purchase of S-400 surface-to-air missile defense systems in defiance of Washington's sanctions, while Beijing has invested heavily in Islamabad, now seeing it as a vital node in the global One Belt, One Road initiative. "It is good for both sides".
Pakistan later aired a video of a man it identified as the Indian pilot.
The clashes came a day after India and Pakistan both accused the other of invading rival airspace, and both claimed to shoot down the other's fighter jets.
The Chinese government's top diplomat, state councillor Wang Yi, spoke by telephone with Pakistan's foreign minister and expressed "deep concern".
"Pakistan, being the weaker country, will be on the receiving end".
Singapore Airlines said on Thursday all of its Europe-bound flights would continue as planned, avoiding the affected airspace as necessary.