A kinetic equation that describes the transverse dynamics of an axisymmetric paraxial relativistic electron beam propagating along an external magnetic field in a gas-plasma medium is derived with allowance for the influence of the self-consistent electromagnetic field on the beam, the effects related to the nonlaminar motion and rotation of the beam electrons at the exit from the injector, and the scattering and energy loss of the beam electrons in their collisions with the neutral particles of the background gas.