  Proton-proton total and elastic cross sections are considered in the
Dakhno-Nikonov eikonal model [L.G. Dakhno, V.A. Nikonov, Eur. Phys. J. A8, 209
(1999)] at ultra-high energies. The model takes into account the quark
structure of hadrons and the gluon structure of the supercritical pomeron that
results in colour screening. The pomeron is considered as an input interaction
term. The model gives a reasonably good description of the preLHC and LHC data
for $pp$ collisions with a growth of the type $\ln^2s$ for total and elastic
cross sections and $(\tau={\bf q}_\perp^2\ln^2s)$-scaling for diffractive
scattering. We present parameters of the supercritical pomeron and provide
predictions for the energy region $\sqrt{s}\sim 10^2-10^4$ TeV.
