  In a recent paper, we have evaluated the $gg\rightarrow gg$ scattering
amplitude in the presence of classical color field generated by the colliding
protons in the leading order approximation within the pQCD. In this work, we
show that this amplitude can be resumed to obtain the classical color field
modified $gg \rightarrow gg$ elastic scattering amplitude. This modified
amplitude is suppressed when the longitudinal momentum fraction, $x$, of the
incident gluon is small. Minijet cross section is calculated using the modified
amplitude. We show that the $pp$ and $\bar{p} p$ cross section from $\sqrt{s} =
5$ GeV to 30 TeV can be described as a sum of a hard component contributed by
the modified minijet model and a soft component due to the exchange of the
pomeron and of the I=0 exchange-degenerate $\omega$ and $f$ trajectories. The
predicted cross section has a $\ln^2 s$ asymptotic behavior which satisfies the
Froissart bound.
