  Very high energy gamma-rays from blazars traversing cosmological distances
through the metagalactic radiation field can convert into electron-positron
pairs in photon-photon collisions. The converted gamma-rays initiate
electromagnetic cascades driven by inverse-Compton scattering off the microwave
background photons. Using a model for the time-dependent metagalactic radiation
field consistent with all currently available far-infrared-to-optical data, we
calculate the cascade contribution from faint, unresolved high- and low-peaked
blazars to the extragalactic gamma-ray background as measured by EGRET. For
low-peaked blazars, we adopt a spectral index consistent with the mean spectral
index of EGRET detected blazars, and the luminosity function determined by
Chiang and Mukherjee (1998). For high-peaked blazars, we adopt template spectra
matching prototype sources observed with air-Cherenkov telescopes up to 30 TeV,
and a luminosity function based on X-ray measurements. The low number of about
20 for nearby high-peaked blazars with a flux exceeding 10^-11 cm^-2 s^-1 above
300 GeV inferred from the luminosity function is consistent with the results
from air-Cherenkov telescope observations. Including the cascade emission from
higher redshifts, the total high-peaked blazar contribution to the observed
gamma-ray background at GeV energies can account up to about 30.
