Eleven men, nine women were killed, officials told Swiss news website 20min.ch.
The Junker JU52 HB-HOT aircraft was built in Germany in 1939 and is now a collectors' item.
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".
Although there were eyewitnesses to the crash, the BBC's Imogen Foulkes says that the investigation into what happened will take time.
Just hours before the Ju-52 crash, a family of four was killed when their small plane went down in the Alps, but it was located further west.
Knech also ruled out the idea that the plane had hit an object, such as a cable or another aircraft.
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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.
The doomed aircraft had departed from Ticino in southern Switzerland and was bound for Duebendorf military airfield near the city of Zurich when it crashed into the mountainside at an altitude of 2,450 meters (8,000 feet) above sea level on the west side of the Piz Segnas mountain shortly before 5 p.m. local time (1500 GMT).
The area around the crash site, which is popular with hikers and skiers and includes a glacier, was closed to the public. Knecht said that while heat can affect an aircraft's performance, experienced pilots could deal with that.
Almost 5,000 Ju-52 planes, a product of Germany's Junkers, were manufactured between 1932 and 1952.
Ju-Air offers "adventure flights" for people wanting to experience Switzerland's landscape from vintage planes. The plane holds 17 passengers, two pilots and a flight attendant.
The incident was the worst in Switzerland for several years, but just one of three plane crashes in the country in the space of eight days. JU-AIR also suspended flights with the remaining two Ju-52s until further notice.