Aims. The objective is to obtain the best possible set of rotational (de)-excitation state-to-state and effective rate coefficients for temperatures up to 1500 K. State-to-state rate coefficients are presented among the 20 lowest levels of para-H2O with H2(j2=1) and $\Delta j_2 = 0, + 2 $, and among the 10 lowest levels of para-H2O with H2(j2=3) and $\Delta j_2 = 0, -2$. Methods. Calculations are performed with the close coupling (CC) method over the whole energy range, using the same 5D potential energy surface (PES) as the one employed in our latest publications on water. We compare our CC results both with thermalized quasi-classical trajectory (QCT) calculations using the same PES and with previous quantum calculations obtained between T=20 K and T=140 K with a different PES. Results. Comparisons with thermalized QCT calculations show factors from 1 to 3. Until recently the only other available set of rate coefficients were scaled collisional rate coefficients obtained with He as a collision partner, and differences between CC and scaled results are shown to be greater than with QCT calculations. The use of the CC accurate sets of rate coefficients might lead to re-estimation of water abundance in the astrophysical whenever models include the scaled H2O-He rate coefficients.