"31 died at the spot and nine died at two hospitals in Kathmandu," police spokesman Manoj Neupane told news agency AFP, adding another 23 were injured.
Live footage posted on Facebook showed the towering columns of smoke rising behind the runway, where another plane stood waiting on the tarmac.
Plumes of black smoke could be seen rising from the football pitch where the plane crashed, to the east of the runway at Nepal's only international airport, in the capital Kathmandu.
"There were 67 passengers and 4 crew members" aboard the plane, said airport spokesman Prem Nath Thakur.
"So far 20 injured have been taken to the hospital. Police and army are trying to cut apart the plane to rescue others," he added.
Emergency vehicles appeared to be heading into the smoke as people watched from a distance or filmed on their mobile phones.
"We are trying to bring the fire under control. Details are awaited," airport spokesman Birendra Prasad Shrestha said, adding that the airport had been shut down and all other flights diverted.
"We're now concentrating on evacuating the passengers," the official added.
Mountainous Nepal is notorious for air accidents. Small aircraft often run into trouble at provincial airstrips.
A Thai Airways flight from Bangkok crashed while trying to land in Kathmandu in 1992 killing all on board. US-Bangla Airlines is a unit of the US-Bangla Group, a U.S. Bangladeshi joint venture company.
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A US-Bangla Airlines passenger plane carrying 71 people crashed on Monday while coming in to land at the airport in the Nepali capital, Kathmandu, an airport official said.
According to an AP report, a police official has said that at least 38 people were killed and 23 injured in the crash.
Victims' bodies have been recovered from the wreckage, an official said. "We just pulled out dead bodies and injured from the debris," government spokesman Narayan Prasad Duwadi told AFP.
Plumes of black smoke could be seen rising from the football pitch where the plane crashed, to the east of the runway at Nepal's only international airport, in the capital Kathmandu.
"There were 67 passengers and 4 crew members" aboard the plane, said airport spokesman Prem Nath Thakur.
"So far 20 injured have been taken to the hospital. Police and army are trying to cut apart the plane to rescue others," he added.
Live footage posted on Facebook showed the towering columns of smoke rising behind the runway, where another plane stood waiting on the tarmac.
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13:35
Witnesses have taken to social media to report seeing the horrific crash at the international airport's runway.
Images posted on social media showing plumes of smoke rising into the air above the runway, with it unclear if anyone has been hurt.
An airport official has reportedly confirmed that the aircraft was a Bangladesh passenger plane which "became unstable" while descending into the airport.
There have been reports that the plane was travelling from Dhaka.
It was not immediately known how many passengers were on board the plane which caught fire.
"We are trying to bring the fire under control. Details are awaited," airport spokesman Birendra Prasad Shrestha said.
One witness wrote on social media: "An Airplane just crashed at the Kathmandu International Airport. I saw it when it happened. OMG!"
Kathmandu Post reported there are suspected casualties after the crash.
Plumes of thick black smoke pictured Kathmandu's International Airport following the reported crash
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