Kantemir Davydov said 15 rescuers have been searching the area where the mountaineers were thought to have gone missing.
The search will continue until nightfall in the mountains, roughly until 6:00 pm.
"After that, work will be stopped and will resume in the morning," he said.
Davydov said the location given by their companions could be inaccurate.
Two of four Polish mountaineers fell into a glacial fissure near Mt. Elbrus, at a height of 4,000 meters above sea level.
"According to the information we have, the fissure is 30 meters deep... The mountaineers are alive and they have a gas burner, so they shouldn't freeze before the rescuers arrive," Davydov said.