We present a general-purpose parameterization of the atomic cluster expansion (ACE) for magnesium. The ACE shows outstanding transferability over a broad range of atomic environments and captures physical properties of bulk as well as defective Mg phases in excellent agreement with reference first-principles calculations. We demonstrate the computational efficiency and the predictive power of ACE by calculating properties of extended defects and by evaluating the P-T phase diagram covering temperatures up to 3000 K and pressures up to 80 GPa. We compare the ACE predictions with those of other interatomic potentials, including the embedded-atom method, an angular-dependent potential, and a recently developed neural network potential. The comparison reveals that ACE is the only model that is able to predict correctly the phase diagram in close agreement with experimental observations.