Onsager-type (Khokhlov-Semenov) theory of the nematic ordering in an athermic system of long polymers, which accounts for two-body interactions only, is extended to take into account three-body interactions. The orientation distribution function, the free energy, the isotropic-nematic coexistence and the spinodal conditions are computed numerically for both persistent wormlike chains and chains with freely joint rigid segments. Even though second virial approximation is known to be asymptotically correct at large values of the polymer segment asymmetry l/d, three-body interactions are shown to cause the nontrivial dependence of the nematic ordering critical concentrations on l/d for the realistic values of l/d. Conditions of applicability of the second virial approximation are analyzed quantitatively.