"We expect to recover more bodies," Krishna Bhandari told Reuters. "The plane has broken into pieces."
There were 72 people on the twin-engine ATR 72 aircraft operated by Nepal's Yeti Airlines, including two infants, four crew members and 10 foreign nationals, said airline spokesman Sudarshan Bartaula.
"We don't know their nationalities," he said. "We are trying to ascertain it."
Hundreds of rescue workers were scouring the hillside crash site.
It was the deadliest crash in Nepal since 1992, the Aviation Safety Network database showed, when a Pakistan International Airlines Airbus A300 crashed into a hillside upon approach to Kathmandu.
The plane was 15 years old, according to flight tracking website FlightRadar24.
The ATR72 is a widely used twin engine turboprop plane manufactured by a joint venture of Airbus and Italy's Leonardo. Yeti Airlines has a fleet of six ATR72-500 planes, according to its website.
Local television showed thick black smoke billowing from the crash site as rescue workers and crowds of people gathered around the wreckage of the aircraft.
Air accidents are not uncommon in Nepal, home to eight of the world's 14 highest mountains, including Everest, as the weather can change suddenly and make for hazardous conditions.
Nepal Prime Minister Pushpa Kamal Dahal has called an emergency cabinet meeting after the plane crash, a government statement said.