Police spokeswoman Anita Senti told reporters that it was with "sad certainty" that "the 20 people aboard perished".
Police in southeastern Graubuenden canton (state) said a several-seater plane crashed Saturday on the Piz Segnas mountain above the Swiss Alpine resort of Flims, striking the mountain's western flank about 2,540 meters (8,330 feet) above sea level.
Officials said Sunday they weren't aware of any distress call made from the plane, adding that the investigation into the crash is expected to be "relatively complex" - though there's no indication of foul play.
Deceased passengers include Swiss citizens and a three-person family from Austria, police say.
It was the first time the airline had experienced an accident that resulted in death or injury to passengers or crew members, Waldmeier said.
Speaking Sunday at a news conference in Flims, he said the vintage plane presumably didn't have the crash-resistant cockpit voice and data recorders that more modern aircraft have.
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Junkers JU-52 planes were manufactured between the 1930s and 1950s.
The cause of the crash is still under investigation.
The aircraft was a Junker JU52 HB-HOT plane, built in Germany in 1939 and now a collectors' item. Its pilots are ex-military and professional pilots, all of them volunteers.
A plane crashed on the Piz Segnas mountain.
"We can not yet explain what led to the tragic accident on Piz Segnas", he said. It has suspended all flights until further notice.
Ju-Air offers "adventure flights" for people wanting to experience Switzerland's landscape from vintage planes.