Nepalnews.com reported the propeller-driven, twin-engine Dornier 9N-AHA-with 16 passengers and a pilot, co-pilot and air hostess went down minutes after taking off from the capital of Kathmandu, bound for the Lukla airport, about about 6:20 a.m.
The victims included seven British tourists, five Chinese and four people from Nepal, the report said.
Lukla is about 80 miles from Kathmandu.
The Dornier was operated by Sita Air.
Many tourists visiting Everest, the world's tallest mountain, fly to the Lukla airstrip before embarking on a two- to three-day trek to the Himalayan peak.
The plane crashed on the banks of Manohara River in Thimi, just outside Kathmandu.
The bodies of all 19 had been taken to the Tribhuvan University Teaching Hospital in Kathmandu.
Xinhua, quoting the airport official, said the plane went down after hitting an eagle.
"The pilots seem to have tried to land it safely on the banks of the river but unfortunately the plane caught fire [when it hit the ground]," the report quoted a senior airport police official as saying.
Britain's Daily Telegraph said the Britons were on a trekking holiday to Mount Everest and were traveling with five Chinese and four Nepali passengers.
The newspaper quoted a spokesman for the airline as saying the plane crashed within 2 or 3 minutes of takeoff.
Eighty-three people have died in crashes in Nepal in the past two years and Britain's Foreign and Commonwealth Office raised concerns about air safety in the country, the report said.
The office said poor weather is a factor in air safety in Nepal but warned, "The British Embassy cannot offer advice about which domestic airlines are safer than others."