Electric dipole moments (EDMs) of nuclear or atomic elements may originate either from the QCD $\theta$-term in the Standard Model or from new CP violation
beyond the Standard Model (BSM). If the strong CP problem arising from the smallness of the QCD $\theta$-parameter is explained by an axion,
the $\theta$-parameter is determined by the axion vacuum value. Yet it can have a nonzero value close to the current experimental bound due to either BSM CP violation at low energy scales or high scale breaking of the Peccei-Quinn (PQ) symmetry caused for instance by quantum gravity effect.
We examine to what extent EDMs can discriminate between these two origins of nonzero axion vacuum value. Our results imply that EDMs can provide information not only on BSM CP violation, but also on the origin of the axion vacuum value, therefore on the UV quality of the PQ symmetry in the axion solution of the strong CP problem.