  We present a model for estimating the blazar contribution to the
extragalactic gamma-ray background (EGRB) in the EGRET energy range. It is
based on inverse-Compton scattering as the dominant gamma-ray production
process in the jets of flat spectrum radio quasars (FSRQs) and BL Lac objects,
and on the unification scheme of radio-loud AGN. Depending on the evolutionary
behaviour of radio-loud AGN, our estimate for the point source contribution to
the extragalactic background emission ranges from about ~20%-40% for a redshift
drop off at Z_{max}=3 to around ~35%-85% for a cutoff at Z_{max}=5. Roughly
70%-90% of the AGN contribution to the EGRB would be due to BL~Lacs/FR I
objects. However, in case of BL Lacs our model parameters are not entirely in
agreement with the results from studies at radio wavelengths indicating
systematical uncertainties whereas our estimate for the FSRQ contribution seems
to be consistent. Thus we end up with two possibilities depending on whether we
underpredict or overpredict the BL Lac contribution: either unresolved AGN can
not account for the entire EGRB or unresolved BL Lacs produce the observed
background.
