It is shown that during low-temperature (300–500 K) intercalation of sodium atoms into thin multilayer graphene and graphite films on rhenium the first graphene layer plays the role of a trap to which atoms coming on the surface diffuse through a graphite film. The intercalation phase of the interlayer space in the graphite bulk is actively filled at a sodium atoms concentration under the first graphene layer close to the maximum possible (2 ± 0.5) × 1014 cm–2. This phase capacity is proportional to the graphite film thickness that can be varied in this work from one graphene layer to ~50 atomic layers. The diffusion energy E d of Na atoms through the graphite film was estimated to be E d ≈ 1.4 eV.