It is known that changes in continental water storage can produce vertical surface deformation, induce crustal stress perturbations and modulate seismicity rates. However, the degree to which local changes in terrestrial water content influence crustal stresses and the occurrence of earthquakes remains an open problem. We show how changes in terrestrial water storage, computed for a ~1000 km^2 basin, focus deformation in a narrow zone, causing horizontal, non-seasonal displacements. We present results from a karstic mountain range located at the edge of the Adria-Eurasia plate boundary system in northern Italy, where shortening is accommodatedacross an active fold-and-thrust belt. The presence of geological structures with highpermeabilities and of deeply rooted hydrologically-active fractures focus groundwater fluxes and pressure changes, generating transient horizontal deformation and perturbations of crustal stress up to 25 kPa, at seismogenic depths. The background seismicity rates appear correlated, without evident temporal delay, with the terrestrial water content in the hydrological basin. Being independent from hydraulic diffusivity, seismicity modulation is likely affected by direct stress changes on faults planes.