[en] We have studied J/ψ production in p bar p collisions at √s = 1.8 TeV with the D0 detector at Fermilab, using a μ⁺μ^- data sample collected during the 1994--1995 collider run. We have measured the inclusive J/ψ production cross section as a function of the J/ψ transverse momentum, p_T^J/ψ, in the central and forward rapidity regions. The cross section dσ/dp_T^J/ψ for |η^J/ψ|<0.6 covers the p_T^J/ψ range from 8 to 20 GeV/c. The new measurements are in a good agreement with the CDF and earlier D0 results. The cross section dσ/dp_T^J/ψ for 2.6 <|η^J/ψ|<3.4 covers the p_T^J/ψ range from 3 to 12 GeV/c. We combine the measurements in the two |η^J/ψ| regions to calculate dσ/dη^J/ψ for p_T^J/ψ > 8 GeV/c. The data are compared with the next-to-leading (NLO) QCD calculations, which take into account different J/ψ production mechanisms