The continuous background seismic activity contains information on the internal state of a volcanic system. Here, we report the influence of major regional tectonic earthquakes (M > 5 in most cases) on such state, reflected as changes in the spectral and dynamical parameters of the volcano continuous seismic data. Although changes do not always occur, analysis of five cases of earthquake-induced variations in the signals recorded at Popocatepetl volcano in central Mexico reveal significant fluctuations following the tectonic earthquakes. External visible volcanic activity, such as small to moderate explosions and ash emissions, were related to those fluctuations. We briefly discuss possible causes of the variations. We conclude that recognition of fluctuations in the dynamical parameters in volcano monitoring seismic signals after tectonic earthquakes, even those located in the far field, hundreds of kilometers away, may provide an additional criterion for eruption forecasting, and for decision making in the definition of volcanic alert levels.