We report a calculation of all two-loop quantum electrodynamics corrections with closed fermion loops for the n=1 and n=2 states of H-like ions and for a wide range of the nuclear charge numbers Z=1-100. The calculation is performed to all orders in the binding-strength parameter Zα, with the exception that in a few cases the free-loop approximation is employed in the treatment of the fermion loops. Detailed comparison is made with previous Zα -expansion calculations and the higher-order remainder term to order α2 (Zα) 6 is identified.