  Very high energy gamma-rays(E>20GeV) from blazars traversing cosmological
distances through the metagalactic radiation field can convert to
electron-positron pairs in photon-photon collisions. The converted gamma-rays
initiate electromagnetic cascades driven by inverse-Compton scattering off the
microwave background photons. The cascades shift the injected gamma ray
spectrum to MeV-GeV energies. Randomly oriented magnetic fields rapidly
isotropize the secondary electron-positron beams resulting from the beamed
blazar gamma ray emission, leading o faint gamma-ray halo. Using a model for
the time-dependent metagalactic radiation field consistent with all currently
available far-infrared-to-optical data, we compute (i) the expected gamma-ray
attenuation in blazar spectra, and (ii) the cascade contribution from faint,
unresolved blazars to the extragalactic gamma-ray background as measured by
EGRET, assuming a generic emitted spectrum extending to an energy of 10 TeV.
The latter cascade contribution to the EGRET background is fed by the assumed
>20 GeV emission from the hitherto undiscovered sources, and we estimate their
dN-dz distribution taking into account that the nearby (z<0.2) fraction of
these sources must be consistent with the known (low) numbers of sources above
300 GeV.
