Several models for the hard X-ray background (XRB) suggest that it is a res
ult of the emission from heavily obscured AGN. Recent studies have revealed
the presence of a new population of hard X-ray sources that must contribut
e significantly to the XRB. However, whether the majority of these sources
are obscured AGN or some other type of object at present remains unclear, H
ere, we further examine the possibility that a significant fraction of the
XRB comes from a population of galaxies undergoing advection-dominated accr
etion in the high-(m) over dot regime and thus produce intrinsically hard s
pectra. When the accretion rate is close to (m) over dot (crit) above which
an advection-dominated accretion flow (ADAF) no longer exists, the major o
r contribution to X-ray emission is from inverse Compton scattering of the
soft seed photons produced by cyclo-synchrotron radiation. In this regime,
the resulting ADAF spectra are relatively hard with a fairly constant X-ray
spectral index alpha similar to 0.2-0.4 and a spectral cut-off at similar
to 200 keV. We show that the integrated emission from such sources can prov
ide a good fit to the hard (> 2keV) X-ray background, provided that the spe
ctrum is dominated by the contribution from objects located at redshifts z
similar to 2-3. The model requires most of the contribution to the XRB to b
e resulting from objects accreting at (m) over dot (crit).