Abstract Ammonia (NH3) is the first polyatomic molecule detected in the interstellar medium. Both its spectroscopic and collisional properties have been extensively studied earlier, and NH3 was often used in laboratory astrophysics studies to compare high-level scattering calculations with state-of-the-art experiments. Nevertheless, some of its important collisional properties remain unresolved. In this paper we report state-to-state and thermally averaged collisional data for the rotational excitation of NH3 by H2 calculated with the close-coupling quantum theory. Both nuclear spin symmetries (ortho/para) of the colliders are studied. Similar research has been carried out previously, providing rate coefficients up to temperature of 200 K for rotational states with internal energy up to ~420 cm−1. Here we have computed cross sections for collision energies up to 4700 cm−1 and rate coefficients up to 500 K. Most of the rotation-inversion levels of ammonia have been considered below the first vibrational excitation threshold, leading to a total of 33 ortho- and 62 para-NH3 states. We have compared our results with the most accurate data for He and H atoms available in the literature. The propensity rules have also been analysed in the case of high rotational levels of NH3. The rate coefficients obtained by averaging over the thermal H2 relative populations exhibit significantly larger magnitudes than the state-to-state collisional data in the case of NH3 transitions with large internal energy difference, when the rotational energy transfer between the colliders is strong.