The article addresses the problem of the connection of earthquakes with geomagnetic phenomena. We have carried out an experimental study using a method based, firstly, on the separation of periods of geomagnetic activity into extremely quiet and disturbed, and, secondly, on the description of seismic activity with an index called the global daily magnitude (GDM). By analyzing the NEIC earthquake catalog of the US Geological Survey over a 20-year period from 1980 to 1999, we have shown that the planetary activity of earthquakes under extremely quiet geomagnetic conditions is noticeably higher than under disturbed conditions. The detected tendency for seismic activity to increase in extremely quiet periods of geomagnetic activity has indirectly been confirmed by the analysis of 35 earthquakes with magnitude 8 and higher, which occurred on Earth from 1980 to 2019. We have found that in extremely quiet geomagnetic conditions, the probability of the occurrence of strong earthquakes is noticeably higher. The result qualitatively confirms the assumption of a change in the regime of seismic activity due to the influence of alternating magnetic fields on the ductility of rocks.