Most all of the Soviet rifles/ammo uses the .310-.312 diameter bullet, this bullet size is also shared with the Japanese 7.7 and .303 British, even the Ak/SKS if your loading up really light loads, I have some x54r training ammo that replicates the x39 round. They are from East Germany, these have a 124 grain bullet, like x39 and duplicate the recoil etc.
About the only Soviet style rifle that could utilize .308 sized bullets are some of the Finnish Mosins that were rebarreled, my Finnish M28/76 could use them. Again, these could be hit or miss, you would need to slug the bore of the respective rifle to find out.