Repeated periods of inflation-deflation in the vicinity of the Svartsengi volcanic system, SW-Iceland, were detected in January-July 2020. We used seismic interferometry to characterize temporal variations of seismic velocities (dv/v). The station closest to the inflation source center (~1km) showed the largest velocity drop (~1%). The frequency-depth analyses, using frequencies between 0.1 to 2 Hz, showed the dv/v are sensitive to changes occurring at depths down to ~4km, which agrees with modeled strain changes. The dv/v correlates with the deformation measurements (GPS, InSAR), over the periods, indicating similar crustal processes. We interpret the velocity drop to be caused by crack opening triggered by intrusive magmatic activity. We have monitored dv/v variations in near real-time for the first time in Iceland during volcanic unrest. We conclude that single-station cross-component analyses provide the most robust solutions which may be useful for early detection of magmatic activity.