Embedded clusters and periodic supercell approaches are used to obtain accurate ab initio values for the parameters of an extended t-J Hamiltonian for multilayered cuprates. In-plane and interplane magnetic coupling constants (J and J⊥) and hopping integrals (t and t⊥) are explicitly considered for various superconducting multilayered cuprates. For YBa2Cu3O6, results are in good agreement with available experimental data thus supporting the reliability of the present extended t-J Hamiltonian parameters. The comparison of the magnitude of the different parameters in the extended t-J model strongly suggests that t⊥ and J⊥ play a key role in defining the differences in the critical temperature of bilayered cuprates.