The reionization of the Universe ends the dark ages that started after the recombination era. In the case of H, reionization finishes around $zsim 6$. Faint star-forming galaxies are the best candidate sources of the H-ionizing radiation, although active galactic nuclei may have also contributed. We have explored whether the termination regions of the jets from active galactic nuclei may have contributed significantly to the ionization of H in the late reionization epoch, around $zsim 6-7$. We assumed that, as it has been proposed, active galactic nuclei at $zsim 6$ may have presented a high jet fraction, accretion rate, and duty cycle, and that non-thermal electrons contribute significantly to the pressure of jet termination regions. Empirical black-hole mass functions were adopted to characterize the population of active galactic nuclei. From all this, estimates were derived for the isotropic H-ionizing radiation produced in the jet termination regions, at $zsim 6$, through inverse Compton scattering off CMB photons. We find that the termination regions of the jets of active galactic nuclei may have radiated most of their energy in the form of H-ionizing radiation at $zsim 6$. For typical black-hole mass functions at that redshift, under the considered conditions (long-lasting, common, and very active galactic nuclei with jets), the contribution of these jets to maintain (and possibly enhance) the ionization of H may have been non-negligible. We conclude that the termination regions of jets from active galactic nuclei could have had a significant role in the reionization of the Universe at $zgtrsim 6$.