Several models for the hard X-ray background (XRB) suggest that it is a result of the emission from heavily obscured AGN. Recent studies have revealed the presence of a new population of hard X-ray sources that must contribute significantly to the XRB. However, whether the majority of these sources are obscured AGN or some other type of object at present remains unclear, Here, we further examine the possibility that a significant fraction of the XRB comes from a population of galaxies undergoing advection-dominated accretion in the high-(m) over dot regime and thus produce intrinsically hard spectra. When the accretion rate is close to (m) over dot (crit) above which an advection-dominated accretion flow (ADAF) no longer exists, the major or 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 provide a good fit to the hard (> 2keV) X-ray background, provided that the spectrum 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 be resulting from objects accreting at (m) over dot (crit).