Numerous flights were cancelled or diverted Wednesday after Pakistan closed its airspace and India shut airports, as soaring tensions between the nuclear-armed rivals stoked fears of a full-blown conflict.

The closures came after Pakistan said it had shot down two Indian Air Force planes in its airspace over disputed Kashmir. India said its forces shot down a Pakistani fighter jet, but also lost one of its own planes.

The air traffic disruption was affecting routes passing through the region that are popular with Western holidaymakers, with an industry body saying that a huge number of flights to Southeast Asia may have to be diverted.

Pakistan's Civil Aviation Authority and the military said the country's entire airspace had been closed, with a CAA source telling AFP that all airlines had been notified to "suspend their operations in Pakistan until further notice".

Pakistan International Airlines, the country's flag carrier, warned that "flights may be affected due to closure of Pakistan commercial air space".

In India, at least six airports were shut - Srinagar, Jammu and Leh in Kashmir and Amritsar, Chandigarh and Dehradun, and a vast area of airspace north of New Delhi was closed to civilian flights.

Scores of flights were cancelled and many between Asia and Europe that would normally fly over Kashmir have been diverted, aviation company officials said on condition of anonymity.

The Aviation Authority of India did not respond to requests for comment.

A map of live air traffic in the area by monitoring group Flight Radar showed almost no flights over Pakistan or in a strip of land across the border on the Indian side.

"International flights that transit between Indian and Pakistani airspace now being affected," the group said on Twitter.

"Some flights returning to origin, while others appear to be seeking alternate routing."

A spokesman for the International Air Transport Association, an industry group representing many of the world's airlines, did not immediately have details about all the affected flights.

But he said about 220 flights usually pass through Pakistani airspace each day between Europe and Southeast Asia.

"Alternative routes are available for the flights impacted by the closure of Pakistan airspace," he said.

India and Pakistan's ties have been under intense strain since a February 14 suicide bombing in Indian Kashmir that killed 40 troops.

Tensions escalate as Indian airstrike hits inside Pakistan

Tensions escalated sharply on the Asian subcontinent Tuesday with nuclear-armed neighbors Pakistan and India trading accusations and warnings after a pre-dawn airstrike by India that New Delhi said targeted a terrorist training camp.

The Feb. 14 attack was the worst on Indian forces since the start of the 1989 insurgency in Kashmir and came as anticipation rises for an Indian general election, which is due by May.

Addressing a rally of former soldiers in the Indian state of Rajasthan hours after the airstrike, Prime Minister Narendra Modi said India was in “safe hands.”

“I vow that I will not let the country bow down,” he said.

Pakistani Foreign Minister Shah Mahmood Qureshi condemned Tuesday’s incursion, saying New Delhi had “endangered” peace in the region for political gains.

Pakistan Prime Minister Imran Khan dismissed India’s account of the airstrike on a terrorist training camp as “self-serving, reckless and fictitious.”

Earlier this month, Khan had authorized the army to “respond decisively and comprehensively to any aggression or misadventure” by India, after New Delhi vowed a “jaw-breaking response” to the Kashmir suicide bombing.

U.S. Secretary of State Mike Pompeo encouraged both countries to exercise restraint and avoid escalation.

A statement from his spokesperson’s office said Pompeo spoke to government ministers of both countries and underscored to Pakistan the urgency of taking meaningful action against terrorist groups on its soil.

Pakistan has vowed to help investigate the suicide bombing and to take action against anyone found to be using Pakistani soil for attacks on India.

It also offered to hold a dialogue with India on all issues, including terrorism.

Kashmir, which is split between the two countries but claimed by each in its entirety, has been the cause of two wars between the neighbors.

They fought a third war in 1979 over East Pakistan, which gained independence with the help of India and became Bangladesh.

Insurgents in Indian-controlled Kashmir have been demanding either outright independence or union with Pakistan.

India routinely accuses Pakistan of arming and training militants who cross the mountainous Himalayan region.

The Pakistan-based militant group Jaish-e-Mohammad claimed responsibility for the suicide bombing. The bomber, who made a video beforehand, was a resident of Indian-controlled sector of Kashmir.

Muhammad Amir Rana, a security analyst and executive director of the Islamabad-based Pakistan Institute of Peace Studies, urged the international community to move quickly to de-escalate tensions.

“It’s quite critical and it is important that the international community intervene quickly to start a peace process between India and Pakistan,” he said, adding that the United States, China and Russia should take the lead.

China, a close ally of Pakistan, urged both sides to show restraint.

“We hope that both India and Pakistan can ... take actions that will help stabilize the situation in the region and help to improve mutual relations,” said China’s Foreign Ministry spokesman Lu Kang.

Pakistan accuses India of cross-border air strikes

Pakistan said Tuesday that Indian warplanes crossed into its airspace over the ceasefire line in Kashmir and dropped payloads, after tensions spiked between the nuclear-armed neighbours over the disputed region.

"Indian Air Force violated Line of Control," Pakistan military spokesman Major General Asif Ghafoor tweeted, referring to the de facto border between Indian- and Pakistani-administered Kashmir.

Pakistan Air Force jets were scrambled in response to the incursion, Ghafoor said.

"Facing timely and effective response from Pakistan Air Force (the Indian aircraft) released payload in haste while escaping near Balakot. No casualties or damage."

He did not provide further information on the location, and whether it was a town of that name in Pakistani-administered Kashmir or further into its territory.

Ghafoor tweeted images of what he said was the payload, showing what appeared to be pieces of metal in a heavily forested area.

There was no immediate comment from New Delhi.

However, Indian news reports said that air force jets hit multiple targets including camps run by Jaish-e-Mohammad, the Islamist group that claimed the February 14 suicide attack in Kashmir that sent tensions soaring.

"Top government sources said that there were nearly 200 casualties from the (Indian Air Force) strike," private broadcaster CNN News 18 said.

New Delhi had threatened to retaliate after the deadliest attack in three decades in Kashmir killed more than 40 Indian paramilitaries.

Islamabad has said it had nothing to do with the attack, and warned it will retaliate if India launches any strike.

JeM is one of several anti-Indian groups fighting in Kashmir, which has been claimed by both India and Pakistan since independence in 1947.

They have fought two of their three wars over the Himalayan territory.

Pakistan's interior ministry announced last week that authorities had seized control of a complex believed to be the JeM headquarters.

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