Interaction energy between two point charges, <$E W sub QQ prime>, or two point dipoles, <$E W sub PP prime>, located in a medium with a constant dielectric permittivity near the plane surface of a metallic or semiconducting substrate with the spatial dispersion of its dielectric function has been revisited. The calculations were made on the basis of the Green's function method for layered systems. Long-range lateral asymptotics were found. The non-local character of screening in the substrates was shown to substantially modify the dependences of <$E W sub QQ prime> and <$E W sub PP prime>, on the distance between the objects concerned. Thus, the purported conventional electrostatic interactions between adsorbed atoms and molecules (modeled by point charges and point dipoles) should be reconsidered making allowance for the substrate polarization. In particular, this factor may significantly influence the structure of electrostatic dipole lattices arising near the surfaces of solids, as well as the kinetics of charge or dipole motion over the surface.

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