The spin correlation coefficients in the neutron-deuteron elastic scattering process at incoming neutron laboratory energies E = 10, 135, 190, and 250 MeV are determined by solving the momentum space three-nucleon (3N) Faddeev equations. The chiral two-nucleon (2N) interaction with momentum-space semi-local (SMS) regularization up to the fifth order of chiral expansion (), supplemented by the F-waves terms from the sixth order (), is used. Additionally, the consistent 3N force (3NF) at the third order of chiral expansion, supplemented by the short-range contributions from is applied. As a results, we give predictions for the complete set of spin correlation coefficients . We find that the effect of the investigated three-nucleon components amounts up to several dozen percent, depending on reaction energy, scattering angle and type of spin correlation coefficient itself. Our results can serve as a guide for future measurements of the spin correlation coefficients.