Magnetic fields due to the magnetospheric ring current, together with their induced counterparts, must be correctly taken into account when modeling the geomagnetic field using modern observatory and satellite measurements. It is common practice to parameterize the induced field using a response function depending on a spherically symmetric electrical conductivity model of the solid Earth. Here we show that Earth's metallic core should be included in such conductivity models, which has not previously been the case. Abrupt changes in the amplitude of the ring current during geomagnetic storms excite a wide range of frequencies, some of which can induce electrical currents in the core. These currents decay very slowly because of the high conductivity of the core; the resulting induced field will therefore not be of zero mean even when averaged over many years. We present the results of time domain numerical simulations of induction that demonstrate the influence of a conducting core in an idealized experiment based on a synthetic geomagnetic storm. Moving to a more realistic scenario we show that taking 50 years of Dst(t) index as an input, an induced field Ist(t) with a mean value (when averaged over 10 years) of up to -1.5 nT is obtained. We conclude that transient induction in the metallic core caused by magnetospheric field variations must be included in accurate portrayals of the near-Earth magnetic environment. Copyright 2011 by the American Geophysical Union.