Hadron-nucleus collisions at CERN LHC energies are studied by including explicitly semihard parton rescatterings in the collision dynamics. Under rather general conditions, we obtain explicit formulas for the semihard cross section and the inclusive minijet transverse spectrum. As an effect of the rescatterings the spectrum is lowered at small p(t) and is enhanced at relatively large transverse momenta, the deformation being more pronounced at increasing rapidity. Its study allows to test the proposed interaction mechanisms and represents an important baseline to examine nucleus-nucleus collisions.