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 sJ and J'd and hopping integrals st and t'd 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.