  The asymptotic behavior of the scattering amplitude for two scalar particles
at high energies with fixed momentum transfers is studied. The study is done
within the effective theory of quantum gravity based on quasi-potential
equation. By using the modified perturbation theory, a systematic method is
developed to find the leading eikonal scattering amplitudes together with
corrections to them in the one-loop gravitational approximation. The relation
is established and discussed between the solutions obtained by means of the
operator and functional approaches applied to quasi-potential equation. The
first non-leading corrections to the leading eikonal amplitude are found.
