Chechen fighters have shot down Russian helicopters in the North Caucasus in the past, but an official said it was too early to say what had caused the crash.
Alexander Baranov, North Caucasus military commander, said: "It seems [the pilot] got disorientated, did not take the right precautionary measures to get out of cloud and clipped the tops of the trees."
An Interfax news report had on Monday quoted an unnamed source as saying 10 of the 15 people on board the Mi-8 helicopter were killed when the it crashed near the town of Vladikavkaz.
The defence ministry said the bodies of three senior officers had been found at the crash site.
Those on board had included the deputy head of logistics for the Russian armed forces, and several of his subordinates.
Colonel Alexander Drobyshevsky said on Monday: "Initial information is that there were 12 passengers and three crew on board the helicopter.
"Five servicemen have been found alive at the crash site. We are trying to establish what happened to the others.
A spokesman for the emergencies ministry in North Ossetia, which includes Vladikavkaz, said: "Rescuers and soldiers are at the scene. The helicopter came down in a hard-to-reach place."
Moscow is fighting an insurgency against its rule in the North Caucasus, centred on the nearby Chechnya region.