The 9N-AKY aircraft crashed as it was trying to land at the airport, which is often regarded as the most dangerous airport in the world.
Lukla, located at an elevation of 2,800 meters, is the gateway to the world's highest peak Mount Qomolangma located in the eastern district Solukhumbu.
"The aircraft crashed just a few meters away from the runway at 1:56 p.m. (local time)," Yogendra Kunwar, chief of the Lukla airport, confirmed to Xinhua over phone.
Following the crash, the rescue operation was carried out immediately by the team of the Nepal Army, police, a rescue team of Goma Airlines and the locals.
Dev Kumar Kathayat, a Nepal Army official who joined the rescue operation, told us The aircraft crashed just in front of my eyes after it entered into the clouds near the runway. We rescued all of the three crew members within an hour of the incident."
Captain Paras Rai was pronounced dead at hospital at 3:20 p.m. local time while the co-pilot was reported to be in critical condition.
Though it has been speculated that the crash occurred owing to bad weather, the exact cause is yet to be identified.
Since the spring climbing expedition falls in April and May, the Lukla airport has been receiving up to 105 flights in a single day.
Around 40 expedition teams comprising 371 climbers from various countries have taken the permit to scale the world's highest peak this season.