The plane crashed in a basin at 2450 metres above sea level on the west side of the Piz Segnas mountain shortly before 5pm on Saturday afternoon.
Police said Sunday they have now determined that all 20 people on board the plane, including its three crew members, died.
An eyewitness told Swiss newspaper 20 Minutes that the "plane turned 180 degrees to the south and fell to the ground like a stone".
"The JU-Air team is deeply saddened and is thinking of the passengers, the crew and families and friends of the victims", JU-Air wrote in a statement on its website Sunday.
On Sunday, Swiss officials said they were unaware that any distress call had been sent out from the plane, and said they expected the investigation into the cause to be "relatively complex".
There were 11 men and nine women aboard, including an Austrian couple and their son, she said.
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The mountainous area in southeastern Switzerland is popular with hikers and skiers and includes a glacier.
Officials can essentially rule out a collision with another aircraft or hitting an obstacle such as a wire, and there's no indication of foul play or that the aircraft lost parts or broke up before the crash, he added. Its pilots are ex-military and professional pilots, all of them volunteers.
The aircraft belongs to JU-Air, a company with links to the Swiss air force, the ATS news agency reported.
The company's flight operations were suspended, it said.
Ju-Air offers "adventure flights" for people wanting to experience Switzerland's landscape from vintage planes.