A metamaterial rod with resonators containing negative-stiffness (NS) mechanisms is proposed for generating very low-frequency bandgaps. The underlying principle employs the NS mechanism (a pair of mutual repelling permanent magnet rings) to partially or totally neutralize the stiffness of the positive-stiffness element (two coil springs) of the resonator and thus to achieve an ultralow, even zero, stiffness, which enables a significant shift of the bandgap from a high frequency to a low one. Experiments on the restoring force feature of the resonator and the bandgap of the metamaterial rod are carried out, which provide sufficient evidence to validate the proposed concept for substantially lowering bandgaps in locally resonant metamaterials. This study opens a potential path to manipulate elastic waves within a very low-frequency range.