The footprints, which the army said measured 81cm by 38cm, were spotted by its mountaineering expedition team on April 9 in the Himalayas near Makalu Base Camp on its way to scale Mount Makalu, the fifth-highest mountain in the world at 8485 metres.
The army responded to some of the criticism by saying it was "prudent to excite scientific temper and rekindle the interest".
Sightings have been reported for centuries. It led many to jocularly speculate whether the Indian Navy would now hunt for the equally elusive and mythical Loch Ness monster, with the IAF too chipping in by chasing UFOs in its fighter jets.
Unsurprisingly, the tweet prompted a flurry of incredulous responses on social media, with many rebuking the Indian military for propagating theories previously debunked by science.
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The Indian Army has, surprisingly, found something that has so far been mostly in the realm of fantasy popular culture - the mythical Yeti.
Many have attempted to locate the creature, including the conqueror of Mount Everest, Sir Edmund Hillary but they all found nothing.
Due to the lack of evidence of the creature's existence, the scientific community has generally regarded the Yeti as a legend.
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In 2013, Oxford University genetics professor Bryan Sykes conducted tests on hair samples left behind in footprints.
One of the pictures put out by the Army showed a large footprint in the snow.