The usefulness of the three-body mechanism of η-meson production is tested by extending to high energies a recently developed two-step model of the pd→3He η reaction by us, which was successful in reproducing the energy dependence of the data near threshold. The η production in this model proceeds in two steps via the pp→πd and πN→ηp reactions with the intermediate particles being off-shell. The finaηl state interaction is incorporated through a T matrix for η3He elastic scattering constructed using few body equations. In a comparison of the calculated angular distributions with some recently available data, we discover the limitations of the model at high energies.