Abstract Eruptions in basaltic volcanoes are often preceded by increasing seismicity and surface deformation, which progressively damage and weaken the volcanic edifice. We show how damage and crack interaction produce the inverse Omori‐Utsu law for earthquakes during pre‐eruptive periods. Rock mass continuity, representing damage, is shown to decrease exponentially with the earthquake number; we interpret it as a general form of the Omori‐Utsu law. Pre‐eruptive earthquake time series are shown to be controlled by heterogeneity distribution, finite‐size effect and crack interaction, and by the feeding system characteristic time. Magma‐edifice coupling is described by state variables that depend on the continuity and the feeding system characteristic time. Pre‐eruptive seismicity of the 2004–2017 24 summit/proximal eruptions of Piton de la Fournaise volcano was well modeled by an inverse Omori‐Utsu law. It allowed identifying two cases: (a) strong crack interaction and earthquake number acceleration, when failure in strong intact rock and finite‐size effects dominate the brittle fracture process; in that case the magma‐edifice interaction power exhibits a maximum before the eruption; (b) weak crack interaction, generating an almost constant earthquake rate and corresponding to a brittle fracture process at constant strain in a weak, fractured rock mass. In this latter case eruptions occurred when the continuity reached a critical value, close to 0.25. Specific times are identified, from the time variations of the state variables; they define estimators that provide values of the eruption time within 10% of the true value in 60%–75% of the cases studied, from the complete time series.