The X-ray radiation from the beam of relativistic particles channeled in a crystal is analyzed in the presense of distributed feedback caused by the Bragg reflection from atomic planes. The theory developed considers the contribution of the beam to the system polarizability tensor. When the beam current density exceeds the so-called threshold value, laser generation starts. The influence of absorption and problem geometry on the threshold value has been studied. It is shown that non-one-dimensional geometry provides a considerably lower generation threshold than the conventional one-dimensional geometry. Estimates of the minimum threshold beam current density and of the number of induced X-ray quanta are given taking into account multiple scattering. The possibility of experimental observation of induced quanta is also discussed.