The tourists from the central Russian city of Yaroslavl left on a trip to the Republic of Adygea, whose capital is about 1,000 miles south of Moscow, on May 1 but never reported back.
Four teams totaling 16 local rescue workers are searching for missing tourists in remote mountainous areas.
Sergei Sergeyev, head of the press service for local emergencies center, said one team had reached the Belaya River, where the tourists were supposed to start a water leg of their trip.
"One of the groups is approaching the upper course of the Belaya River, to the starting point of their [the missing tourists'] water route," he said. "Two other groups are heading to designated areas; they need about 24 hours to get there."
The official said rescuers could not use a helicopter in the search because of bad weather.