We study the sensitivity reach of the gamma-ray method for measurement of relatively strong cosmological magnetic field with strength in the 1-10 pG range using deep exposure of the nearest hard spectrum blazar Mrk 501 with CTA telescopes. We show that the gamma-ray measurement technique can sense the primordial magnetic field with a strength of up to 10^{−11} G. Combination of the cosmic microwave background and gamma-ray constraints can thus sense the full range of possible cosmological magnetic fields to confirm or rule out their relevance to the problem of the origin of cosmic magnetic fields, as well as their influence on recombination and reionization epochs.