India and Pakistan exchanged gunfire through the night in the disputed Himalayan region of Kashmir, a day after Islamabad said it shot down two Indian warplanes and captured a pilot.
There were no immediate reports of casualties, although jet fighters roared over the mountainous region as villagers along the so-called Line of Control fled to safety.
Members of Indian prime minister Narendra Modi's Bharitiya Janata Party called for more military action, suggesting the conflict could worsen.
Pakistan's prime minister Imran Khan called for talks between the two nuclear-armed rivals in a televised address on Wednesday, saying: "Considering the nature of the weapons that both of us have, can we afford any miscalculation?"
World powers have called on the nations to de-escalate the tensions gripping the contested region since a February 14 suicide car bombing killed more than 40 Indian paramilitary personnel.
India responded with an air strike on Tuesday inside Pakistan, the first such raid since the two nations' 1971 war over territory that later became Bangladesh.
The situation escalated with Wednesday's aerial skirmish, as Pakistan said it had shot down two Indian aircraft, one of which crashed in the Pakistan-held part of Kashmir and the other in India-controlled Kashmir.
India acknowledged one of its MiG-21s, a Soviet-era fighter jet, was "lost" in skirmishes with Pakistan and that its pilot was "missing in action".
India also said it shot down a Pakistani plane, something Islamabad denied.
Pakistan's military later circulated a video of a man who identified himself as the Indian pilot, sipping tea and responding to questions, mostly by saying: "You know I can't answer that."
He appeared in good health as he was questioned about his home town, his aircraft and his mission.
Indian and Pakistani officials reported small-arms fire and shelling along the Kashmir region into Thursday.
Government buildings in Muzafarabad, the capital of the Pakistan-controlled section of Kashmir, were used to provide shelter to those who fled from border towns.
Indian army spokesman Lieutenant Colonel Devender Anand described the intensity of the firing as "lesser" than previous nights.
Authorities in Pakistani-controlled Kashmir closed all schools and colleges in the region and urged parents to keep their children at home amid mounting tension. Pakistan's air space remained closed for a second day Thursday, snarling air traffic.
India's finance minister Arun Jaitley suggested at a news conference that Indian special forces carry out secret missions to capture terrorist leaders in Pakistan, invoking the 2011 US Navy Seal operation to kill al Qaida leader Osama bin Laden.
"I remember when US Navy Seals went to Abbottabad to kill Osama bin Laden, then why can't India?" he asked. "This used to be only an imagination, a wish, a frustration and disappointment. But it's possible today."
The violence on Wednesday marked the most serious escalation of the long-simmering conflict since 1999, when Pakistan's military sent a ground force into Indian-controlled Kashmir at Kargil. That year also saw an Indian fighter jet shoot down a Pakistani naval aircraft, killing all 16 on board.
Kashmir has been claimed by both India and Pakistan since almost immediately after their creation in 1947. The countries have fought three wars against each other, two directly dealing with the disputed region.