The interaction of high-energy electrons, positrons, and photons with intense laser pulses is studied in head-on collision geometry. It is shown that electrons and/or positrons undergo a cascade-type process involving multiple emissions of photons. These photons can consequently convert into electron-positron pairs. As a result charged particles quickly lose their energy developing an exponentially decaying energy distribution, which suppresses the emission of high-energy photons, thus reducing the number of electron-positron pairs being generated. Therefore, this type of interaction suppresses the development of the electromagnetic avalanche-type discharge, i.e., the exponential growth of the number of electrons, positrons, and photons does not occur in the course of interaction. The suppression will occur when three-dimensional effects can be neglected in the transverse particle orbits, i.e., for sufficiently broad laser pulses with intensities that are not too extreme. The final distributions of electrons, positrons, and photons are calculated for the case of a high-energy e-beam interacting with a counterstreaming, short intense laser pulse. The energy loss of the e-beam, which requires a self-consistent quantum description, plays an important role in this process, as well as provides a clear experimental observable for the transition from the classical to quantum regime of interaction. © 2013 American Physical Society.