  In the framework of the Higgs inflation, we consider the electromagnetic
field nonminimally coupled to gravity via the parity-preserving $\propto
RF^{2}$ and parity-violating $\propto RF\tilde{F}$ terms. Using the
perturbation theory to the leading order in these couplings, we study the
generation of the electromagnetic field during the inflation stage. We derive
the effective kinetic and axial coupling functions arising in the Einstein
frame in the usual metric as well as Palatini formulations of gravity. For both
formulations, we determine the power spectrum, energy density, and helicality
of the generated electromagnetic fields for different values of the nonminimal
coupling constants. Finally, we estimate the maximal present-day magnitude of
the magnetic field as $10^{-14}-10^{-15}\,$G with the correlation length of
order 10 pc.
