We report on measurements of the inclusive jet production cross section as a function of the jet transverse momentum in pp̅ collisions at √s=1.96 TeV, using the kT algorithm and a data sample corresponding to 1.0 fb-1 collected with the Collider Detector at Fermilab in run II. The measurements are carried out in five different jet rapidity regions with |yjet|<2.1 and transverse momentum in the range 54<pTjet<700 GeV/c. Next-to-leading order perturbative QCD predictions are in good agreement with the measured cross sections.