There were 71 people on board the US-Bangla Airlines plane arriving from Dhaka when it clipped the fence at Kathmandu and burst into flames, said Raj Kumar Chettri, the general manager of the hill-ringed airport.
Those aboard included 33 Nepali passengers, with 32 from Bangladesh, one from China and one from the Maldives.
The accident was the latest to hit mountainous Nepal, which has a poor record of air safety. Small aircraft ply an extensive domestic network and often run into trouble at remote airstrips.
"We have recovered 50 dead bodies so far," said army spokesman Gokul Bhandari.

Source: AAP
Chettri said that moments after the plane received permission to land, the pilot said he wanted to go in a northern direction. Asked by the control tower if there was a problem, he replied in the negative.
The plane was then seen making two rounds in a north east direction, Chettri said. Traffic controllers again asked the pilot if things were OK, and he replied, "Yes".
The tower then told the pilot his alignment was not correct, but there was no reply, Chettri added.
"The plane should have come from the right direction," Chettri said, adding that it hit the airport fence, touched the ground and then caught fire.
Survivor Sanam Shakya, who climbed out of a window of the smouldering plane, said he didn't realise the aircraft was in trouble until it hit the ground.
"The plane was going up down, right and left, up down... so I thought that was some air traffic only. But I came to know that the aircraft had a problem only when it forcibly landed," the 33-year-old said from a hospital bed.
It was not immediately clear if the pilot had issued a "Mayday" call, or distress signal.

A plane has crashed at TIA in Nepal. Source: Twitter: @pdpbasyal
Meanwhile, the CEO of US-Bangla Airlines Imran Asif laid blame on Kathmandu's air traffic control, saying the controller "fumbled" the landing.
"Our pilot is an instructor of this Bombardier aircraft. His flight hours are over 5,000 hours. There was a fumble from the control tower," Asif told reporters outside the airline's offices in Dhaka.
An airport source, who spoke on condition of anonymity, said there may have been confusion between air traffic control and the pilot over which end of Kathmandu's sole runway -- referred to as 'Runway 02' and 'Runway 20' -- the plane was meant to land on.
A recording purportedly of the conversation between the controller and pilot has been published online. AFP could not independently verify the recording.

A picture taken with a phone shows rescue teams next to a wreckage of a plane that crashed at the main airport Tribhuvan International Airport in Kathmandu. Source: EPA
Eyewitnesses said the plane, a Canadian-made Bombardier Dash 8 Q400 turboprop, crashed as it made a second approach towards the airport, shuddering violently as it lost height before hitting the ground and bursting into flames.
"It should have come straight but it went in the other direction... then it crashed towards the field," said airport cleaner Sushil Chaudhary, who saw the crash.

Source: Google Maps
'Challenging terrain'
Desperate relatives searched for the names of their loved-ones on a list of casualties hung outside a hospital where most of the victims were taken. One woman collapsed in tears after checking the list.
Another bewildered-looking survivor, 27-year-old Basanta Bohara, told AFP at a hospital that he couldn't remember how he escaped from the burning wreckage.
"I remember the accident. Nothing else. I don't know how I got out," Bohara said.
Airline spokesman Kamrul Islam said 33 of the passengers were Nepali, 32 were Bangladeshi, one each from China and the Maldives. Local media reported that many of the Nepali passengers were college students returning home for a holiday.
Kathmandu airport briefly closed after the accident, forcing inbound flights to divert, but it has since reopened.
It is Nepal's only international airport and experts say the mountainous landscape with the towering Himalayas to the north poses difficulties for pilots coming in to land.
"The landing at Kathmandu because of the terrain is a little challenging," said Gabriele Ascenzo, a Canadian pilot who runs aviation safety courses in Nepal.
Depending on the direction of approach, pilots have to fly over high terrain before making a steep descent towards the airport, Ascenzo added.
The accident is the deadliest since September 1992, when all 167 people aboard a Pakistan International Airlines plane were killed when it crashed as it approached Kathmandu airport.
Just two months earlier, a Thai Airways aircraft had crashed near the same airport, killing 113 people.
Nepal's poor air safety record is largely blamed on inadequate maintenance and substandard management. Accidents are common and Nepal-based airlines are banned from flying in European Union airspace.
The Dhaka-based US-Bangla Airlines launched just four years ago and made its first international flight in May 2016 to Kathmandu. It has since expanded with routes to South Asia, the Middle East and Southeast Asia.
In 2015 one of its planes overshot the runway on landing at Saidpur in northwest Bangladesh. There were no reports of injuries.