The energetic electrons of the inner radiation belt during a geomagnetic disturbance can penetrate in the forbidden range of drift shells located at the heights of the topside equatorial ionosphere (< 1000 km). A good correlation was previously revealed between positive ionospheric storms and intense fluxes of quasi-trapped 30-keV electrons at ~900 km height in the forbidden zone. In the present work, we use statistics to validate an assumption that the intense electron fluxes in the topside equatorial ionosphere can be an important source of the ionization in the low-latitude ionosphere. The data on the energetic electrons were obtained from polar orbiting satellites over the periods of the 62 strong geomagnetic storms from 1999 to 2006. Ionospheric response to the selected storms was determined using global ionospheric maps of vertical total electron content (VTEC). A case-event study of a major storm on 9 November 2004 provided experimental evidence in support to the substantial ionization effect of energetic electrons during positive ionospheric storms at the low latitudes. Statistical analysis of nine magnetic storms indicated that the VTEC increases coincided with and coexisted with intense 30-keV electron fluxes irrespective of local time and phase of geomagnetic storm. We concluded that extremely intense fluxes of the 30-keV electrons in the topside low-latitude ionosphere can contribute ~ 10 - 30 TECU to the localized positive ionospheric storms.