A furious backlash erupted in India Saturday over a video of an Indian pilot shot down by Pakistan praising his captors, as deadly tensions simmered between the neighbours with fierce shelling across their Kashmir frontier.

A string of violent escalations have pushed India and Pakistan to the brink of conflict, sparking global alarm and calls for restraint between the nuclear-armed neighbours.

Pakistan's Prime Minister Imran Khan called for talks with India Wednesday and warned of a catastrophe should the conflict between the nuclear-armed rivals continue to escalate.

Pakistan and India said Wednesday they had shot down each other's warplanes, in a dramatic escalation of the dangerous confrontation between the nuclear-armed rivals.

India and Pakistan have fought two wars and countless skirmishes over Kashmir, the Himalayan region claimed in full by both nuclear-armed rivals.

Pakistan says Indian aircraft crossed into its territory and dropped bombs on Tuesday without causing casualties, in the latest escalation between the nuclear-armed rivals since a deadly attack on Indian troops in the disputed Kashmir region sent tensions soaring.

Maj. Gen Asif Ghafoor, a military spokesman, said the Indian "aircrafts" crossed into the Pakistan-controlled Muzafarabad sector of Kashmir, which is split between the two countries but claimed by each in its entirety. He said Pakistan scrambled fighters and the Indian jets "released payload in haste," near Balakot, on the edge of Pakistani-ruled Kashmir.

Junaid Ayub Rather cowered alongside 30 other students in a small room for two nights while mobs chanted for their blood outside, before finally escaping the rage sweeping India after last week's suicide bombing in Kashmir.

Saudi Arabia's Crown Prince Mohammed bin Salman and Indian leader Narendra Modi vowed Wednesday to increase pressure on countries that fuel terrorism.

India on Tuesday demanded that rival Pakistan take "credible and visible action" over a major suicide attack in Kashmir as it sternly rebuffed Prime Minister Imran Khan's offer to investigate the bombing.

Pakistan is ready to help India investigate the deadliest blast in Kashmir in decades, but will retaliate if Delhi attacks, Prime Minister Imran Khan said Tuesday as tensions between the nuclear-armed rivals soared.