  We study the gauge dependence of the effective average action Gamma_k and
Newtonian gravitational constant using the RG equation for Gamma_k. Then we
truncate the space of action functionals to get a solution of this equation. We
solve the truncated evolution equation for the Einstein gravity in the De
Sitter background for a general gauge parameter alpha and obtain a system of
equations for the cosmological and the Newtonian constants. Analyzing the
running of the gravitational constant we find that the Newtonian constant
depends strongly on the gauge parameter. This leads to the appearance of
antiscreening and screening behavior of the quantum gravity. The resolution of
the gauge dependence problem is suggested. For physical gauges like the
Landau-De Witt gauge the Newtonian constant shows an antiscreening.
