It later said in a statement that a military investigation was underway but "there is little hope that the crew survived the accident."
Swiss Air Force Commander Lt. Aldo Schellenberg told reporters the plane was one of two F/A-18s that had taken off from the Meiringen air base in Bern canton (state) on a training mission in which they were to engage in air policing and combat.
The other plane, a one-seater, returned safely to Meiringen later.
Armed Forces Chief Lt. Gen. Andre Blattmann said the images collected so far from the crash raised fears that the two people aboard had died.
"There's no hard evidence, but we cannot be confident," he said.
The military officials said the fighter jet was unarmed and the pilots appear to have been surprised by poor visibility when the aircraft hit a cliff overlooking Lake Alpnach.
The defense department said in a statement that the flight data recorder had not yet been found, so officials were still in the dark about details such as whether the ejector seats were activated, but all flights with the F/A-18s were temporarily suspended.
Helicopters, military and emergency services were sent to the crash site to search for the crew and put out the fire. A nearby railway line and road were closed.
In the late 1990s, the Swiss Air Force purchased 34 American F/A-18s from manufacturer McDonnell Douglas, now Boeing. This is the second crash involving one of the fleet, and the 32 that remain form the core of the Swiss military's air power.
The last F/A-18 crash in the Swiss Air Force occurred in 1998 in the Swiss Alps, killing the two pilots and injuring several other people.