  It is assumed that the unresolved fraction of the X-ray background (XRB)
consists of a truly diffuse component and a population of the weak sources
below the present detection threshold. Albeit these weak sources are not
observed directly, their collective nature could be investigated by statistical
means. The goal is to estimate the source counts below the conventional
detection limit in the Chandra Deep Field-South 2Ms exposure. The source number
counts are assessed using the nearest neighbor statistics applied to the
distribution of photon counts. The method is described in the first paper of
these series. The source counts down to 3-4 x 10^{-18} cgs in the soft band
(0.5-2 keV) and down to 2-3 x 10^{-17} cgs in the hard band (2-8 keV) are
evaluated. It appears that in the soft band the source counts steepen
substantially below ~10^{-16} cgs. Assuming that the differential slope b =
-1.5 to -1.6 in the range 10^{-16} - 10^{-14} cgs, the number of weaker sources
indicates the slope of approx. -2.0. The steepening is not observed in the hard
band. Steepening of counts in the soft band indicates a new population of
sources. A class of normal galaxies at moderate redshifts is a natural
candidate.
