Primordial magnetic fields of cosmologically interesting field strengths can be generated from gravitationally coupled electrodynamics during inflation. As the cosmological constraints require this to be power law inflation it is not possible to generate at the same time the curvature perturbation from inflation. Therefore here a completion is considered whereby the large scale magnetic field is generated during inflation and the primordial curvature mode in a subsequent era from a curvaton field. It is found that constraints on the model to obtain strong magnetic fields and those to suppress the amplitude of the curvature perturbation generated during inflation can be simultaneously satisfied for magnetic seed fields Bs 10-30 G.
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