Besides the four crew members, there were 67 passengers - 32 Bangladeshis, 33 Nepalis, one Chinese and one Maldivian, airport official Bharat Rawal said.
An airline official said some injured passengers had been taken away by ambulance.
"I can't say exactly how many have been rescued", Mohammed Selim, the airline's manager in Kathmandu, told Dhaka-based Somoy TV station.
Rescue and emergency teams are at the scene.
Dhaka but when the plane approached the Tribhuvan International Airport (TIA) for landing in Kathmandu, the aircraft began to behave strangely.
The plane, which was carrying 71 people, was "out of control" as it came in to land, according to airport authorities. They all had gone to Bangladesh for training.
A recording of conversations between the pilot and air traffic controllers indicated confusion over which direction the plane should land. The two pilots and two cabin crew were Bangladeshi nationals.
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.More news: International Solar Alliance drops limits on membership
A US-Bangla Airlines Flt BS211, a DHC-8-Q400 (S2-AGU) has crashed on landing at Kathmandu, Nepal, during a thunderstorm.
There is silence for a while, then a "Fire One Station" calls the ATC, indicating that a crash has occurred and the airport fire tender is active.
"Certainly each accident is isolated to its own circumstances so it would be inappropriate to comment on any links between or just assume or speculate while both investigations are ongoing", Masluch said in a separate interview.
Amanda Summers, an expat living in Kathmandu, happened to see the crash and described the incident to CNN.
US-Bangla Airlines is a private carrier that launched in July 2014 with the motto "Fly Fast Fly Safe", according to its website. "All of a sudden there was a blast and then another blast".
The airline, part of US-Bangla Group, is based in the Bangladeshi capital, Dhaka, and flies to several domestic and worldwide destinations.
"It was flying very low", said Keyal, a medical student.
The most fatal accident was reported from Kathmandu on Monday, where over 50 people onboard a flight from Bangladesh were killed.