Narendra Modi has accused his country’s enemies of “trying to destabilise us” and vowed that India would “fight, live, work and win as one” in his first remarks since the downing of aircraft over Kashmir on Wednesday morning.

Though he did not mention Pakistan by name, the prime minister suggested “the world is observing” India’s response to the rising tensions between the two countries.

Mr Modi said it was crucial that nothing be allowed to undermine faith in India’s armed forces - “that our enemies don't get the chance to question us”.

The prime minister was addressing a large rally of supporters for his ruling Bharatiya Janata Party (BJP) via video conference from Delhi.

All eyes are on India’s response after a dogfight in the skies over disputed Kashmir in which India says one Pakistani and one Indian fighter jet were shot down. Pakistan says it shot down two Indian planes and denies any losses.

Pakistan shoots down Indian fighter jets: Reaction in pictures Show all 28 1 /28 Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistan shoots down Indian fighter jets: Reaction in pictures Activists of Al-Badr Mujahideen, an islamic militant group, burn an effigy of Indian Prime Minister Narendra Modi during an anti-India protest in Peshawar, Pakistan AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures A Pakistani girl holds a light candle during a vigil for peace in Lahore on March 3 AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures School children react as they celebrate the release of Indian Air Force pilot Wing Commander Abhinandan Varthaman by Pakistan at a school in Ahmedabad Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Indian pilot, Wing Commander Abhinandan, stands under armed escort near Pakistan-India border in Wagah Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Indian Border Security Force soldiers patrol along the border with Pakistan EPA Pakistan shoots down Indian fighter jets: Reaction in pictures A videograb allegedly shows the captured Indian Air Force pilot in the custody of Pakistani military SWNS Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani civil society activists hold anti-war signs during a peace rally in Islamabad AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani civil society activists hold anti-war signs during a peace rally in Islamabad AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures Activists of Al-Badr Mujahideen, an islamic militant group, burn an effigy of Indian Prime Minister Narendra Modi during an anti-India protest in Peshawar, Pakistan Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Kashmiri villagers look on at the smouldering wreckage of an Indian fighter jet after it was shot down by the Pakistani military AP Pakistan shoots down Indian fighter jets: Reaction in pictures Indian soldiers and Kashmiri onlookers stand look on as an Indian army helicopter lands near the site where an Indian Air Force jet was shot down by the Pakistani military AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures An Indian soldier gestures near the wreckage of an Indian Air Force fighter jet that was shot down by the Pakistani military AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures Supporters of a Pakistani religious group Islami Jamiat-e-Talaba brand Indian Prime Minister Narendra Modi a terrorist at a rally to condemn Indian aggression AP Pakistan shoots down Indian fighter jets: Reaction in pictures Indian soldiers and Kashmiri villagers look on at the smouldering wreckage of an Indian fighter jet after it was shot down by the Pakistani military AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures India's Border Security Force soldiers patrol along the fenced border with Pakistan on February 26 Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Protesters in Pakistan march against Indian Prime Minister Narendra Modi after the Indian airstrike on allege Pakistan terrorist camp EPA Pakistan shoots down Indian fighter jets: Reaction in pictures Supporters of India's ruling Bhartiya Janta Party workers hold Indian flags as they celebrate the Indian airstrike on allege Pakistan terrorist camp AP Pakistan shoots down Indian fighter jets: Reaction in pictures Protesters in Pakistan march against Indian Prime Minister Narendra Modi after the Indian airstrike on allege Pakistan terrorist camp EPA Pakistan shoots down Indian fighter jets: Reaction in pictures People in India burn an effigy that represents Pakistan as they celebrate the Indian airstrike on allege Pakistan terrorist camp Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Indian soldiers and Kashmiri villagers look on at the smouldering wreckage of an Indian fighter jet after it was shot down by the Pakistani military AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures Bhartiya Janta Party workers hold Indian flags as they celebrate the Indian airstrike on allege Pakistan terrorist camp EPA Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani Kashmiris in the border town of Chakoti walk past India-bound cargo trucks that are parked as the road to India is closed AP Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani Army soldiers escort journalists to the scene where Indian fighter jets struck in a violation of Pakistani airspace EPA Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani Army soldiers escort journalists to the scene where Indian fighter jets struck in a violation of Pakistani airspace EPA Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani Army soldiers escort journalists to the scene where Indian fighter jets struck in a violation of Pakistani airspace EPA Pakistan shoots down Indian fighter jets: Reaction in pictures Workers enter a concrete bunker that they have built in a residential area near the border Reuters Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani soldiers and journalists gather at the site where Indian fighter jets struck in a violation of Pakistani airspace AFP/Getty Pakistan shoots down Indian fighter jets: Reaction in pictures Pakistani soldiers and journalists gather at the site where Indian fighter jets struck in a violation of Pakistani airspace AFP/Getty

The Pakistani prime minister Imran Khan has urged calm and invited Mr Modi to engage in talks, saying that “better sense must prevail” between the two nuclear-armed countries.

In his video address, Mr Modi praised the armed forces and said India’s “brave soldiers are showing their valour at the border and beyond”.

That appeared to be a reference to heavy gunfire across the Kashmir line of control, the de facto border in the disputed region, since Wednesday’s aerial engagement and the preceding Indian airstrikes on what it described as a militant training camp in Pakistan.

On Thursday morning troops from the two countries briefly exchanged fire in Poonch, a district in Indian-administered Kashmir, according to a statement from the Indian army.

"The Indian army retaliated strongly and effectively," said Lieutenant Colonel Devender Anand, a defence ministry spokesman.

The firing, that India claims was initiated by Pakistan and lasted for a little over an hour beginning at 6am local time (12.30am GMT), was nonetheless significantly less fierce than the artillery fire exchanged by the two sides on Wednesday.

International powers, including the US and China, have urged the two countries to exercise caution and deescalate tensions, which have been rising since the bombing of an Indian paramilitary convoy in Kashmir on 14 February caused the heaviest casualties in the region’s 30-year insurgency.

At a news conference in Hanoi regarding his failed nuclear talks with Kim Jong-un, the US’s Donald Trump said American diplomats had been mediating between the two sides.

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