In this paper an attempt is made to verify the hypothesis on the role of geomagnetic disturbances as a factor determining the intensity of traveling ionospheric disturbances (TIDs). To improve the statistical validity of the data, we have used the based on the new GLOBDET technology method involving a global spatial averaging of disturbance spectra of the total electron content (TEC). To characterize the TID intensity quantitatively, we suggest that a new global index of the degree of disturbance should be used, which is equal to the mean value of the rms variations in TEC within the selected range of spectral periods (of 20-60 min in the present case). It was found that power spectra of daytime TEC variations in the range of 20-60 min periods under quiet conditions have a power-law form, with the slope index k = -2.5. With an increase of the level of magnetic disturbance, there is an increase in total intensity of TIDs, with a concurrent kink of the spectrum caused by an increase in oscillation intensity in the range of 20-60 min. It was found that an increase in the level of geomagnetic activity is accompanied by an increase in total intensity of TEC; however, it correlates not with the absolute level of Dst, but with the value of the time derivative of Dst (a maximum correlation coefficient reaches -0.94). The delay of the TID response of the order of 2 hours is consistent with the view that TIDs are generated in auroral regions, and propagate equatorward with the velocity of about 300-400 m/s.