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"Two people died on the spot and the third one died while undergoing treatment in a hospital in Kathmandu", airport official Pratap Babu Tiwari told Reuters.
Tenzing-Hillary airport is often referred to as the world's most risky airport because of the short runway and hard approach.
The crash occurred while the plane, a Twin Otter belonging to Summit Air, was trying to take off from Lukla for Kathmandu on Sunday morning, said aviation official Raj Kumar Chhetri.
The airport, which is also known by the name of its host town, Lukla, was shut down after the incident.
In addition to the three fatalities, there were four people injured and airlifted to Kathmandu by helicopter.
Among the dead were the plane's co-pilot and two police officers who were near the parked helicopter, said Nepal police spokesman Uttam Raj Subedi.
Lukla airport is the nearest airport to Mount Everest, while April-May is the peak climbing season in the Himalayan country.
It's believed a small plane crashed into a helicopter while taking off from an airstrip. It has been reported that the Summir Air plane was en route to Kathmandu from Lukla.