Previously, it has been shown that long-distance migrants, garden warblers (Sylvia borin), were disoriented in the presence of narrow-band oscillating magnetic field (1.403 MHz OMF, 190 nT) during autumn migration. This agrees with the data of previous experiments with European robins (Erithacus rubecula). In this study, we report the results of experiments with garden warblers tested under a 1.403 MHz OMF with various amplitudes (∼0.4, 1, ∼2.4, 7 and 20 nT). We found that the ability of garden warblers to orient in round arenas using the magnetic compass could be disrupted by a very weak oscillating field, such as an approximate 2.4, 7 and 20 nT OMF, but not by an OMF with an approximate 0.4 nT amplitude. The results of the present study indicate that the sensitivity threshold of the magnetic compass to the OMF lies around 2-3 nT, while in experiments with European robins the birds were disoriented in a 15 nT OMF but could choose the appropriate migratory direction when a 5 nT OMF was added to the stationary magnetic field. The radical-pair model, one of the mainstream theories of avian magnetoreception, cannot explain the sensitivity to such a low-intensity OMF, and therefore, it needs further refinement.