  We consider a Schwarzschild type solution in the discrete Regge calculus
formulation of general relativity quantized within the path integral approach.
Earlier, we found a mechanism of a loose fixation of the background scale of
Regge lengths. This elementary length scale is defined by the Planck scale and
some free parameter of such a quantum extension of the theory. Besides, Regge
action was reduced to an expansion over metric variations between the
tetrahedra and, in the main approximation, is a finite-difference form of the
Hilbert-Einstein action. Using for the Schwarzschild problem a priori general
non-spherically symmetrical ansatz, we get finite-difference equations for its
discrete version. This defines a solution which at large distances is close to
the continuum Schwarzschild geometry, and the metric and effective curvature at
the center are cut off at the elementary length scale. Slow rotation can also
be taken into account (Lense-Thirring-like metric). Thus we get a general
approach to the classical background in the quantum framework in zero order: it
is an optimal starting point for the perturbative expansion of the theory;
finite-difference equations are classical, the elementary length scale has
quantum origin. Singularities, if any, are resolved.
