We investigate the origin of the diffuse 6.4 keV line emission recently detected by Suzaku and the source of H2 ionization in the diffuse molecular gas of the Galactic center (GC) region. We show that Fe atoms and H2 molecules in the diffuse interstellar medium of the GC are not ionized by the same particles. The Fe atoms are most likely ionized by X-ray photons emitted by Sgr A* during a previous period of flaring activity of the supermassive black hole. The measured longitudinal intensity distribution of the diffuse 6.4 keV line emission is best explained if the past activity of Sgr A* lasted at least several hundred years and released a mean 2-100 keV luminosity >~ 1038 erg s-1. The H2 molecules of the diffuse gas cannot be ionized by photons from Sgr A*, because soft photons are strongly absorbed in the interstellar gas around the central black hole. The molecular hydrogen in the GC region is most likely ionized by low-energy cosmic rays, probably protons rather than electrons, whose contribution into the diffuse 6.4 keV line emission is negligible.