[en] A generalized dynamo equation in the first order torsion Garcia de Andrade L C (2012 Phys. Lett. B 711 143) has previously been derived. From this equation it is shown that for the 10 kpc scale, torsion gravity is not able to help seed galactic dynamos since the dynamo time is not long enough to take into account structure formation. In this paper, the dynamo equation is extended to second-order torsion terms—but unfortunately, the situation is even worse and the torsion does not seem to help dynamo efficiency. Nevertheless, in the intergalactic magnetic field scale of 1 mpc, the efficiency of the self-induction equation with torsion changes, and even in the first-order torsion case, one obtains large-scale magnetic fields with 10"9 yr dynamo efficiency. Dynamo efficiency in the case of interstellar matter (ISM) reaches a diffusion time of 10"1"3 yr. This seems to be in contrast with a recent investigation by Bamba et al (2012 J. Cosmol. Astropart. Phys. JCAP05(2010)08) where they obtained, from another type of torsion theory called teleparallelism (A Einstein, Math Annalen (1922)), a large scale intergalactic magnetic field of 10"−"9 G. If this is not a model-dependent result, there is an apparent contradiction that has to be addressed. It is shown that for dynamo efficiency in astrophysical flow without shear, a strong seed field of 10"−"1"1 G is obtained, which is suitable for seeding galactic dynamos. As an example of a non-parity-violating dynamo equation, a magnetic field of the order of 10"−"2"7G is obtained as a seed field for the galactic dynamo from the theory of Einstein’s unified teleparallelism. This shows that in certain gravity models, torsion is able to enhance cosmological magnetic fields in view of obtaining better dynamo efficiency. To better compare our work with Bamba et al (2012 J. Cosmol. Astropart. Phys. JCAP05(2010)08), we consider the slow decay of magnetic fields in the teleparallel model. (paper)