We present results from numerical simulations of the interaction of internal gravity waves (IGW) with magnetic fields in the radiative interior of the Sun. In this second paper, the waves are forced self-consistently by an overlying convection zone and a toroidal magnetic field is imposed in the stably stratified layer just underneath the convection zone. Consistent with the results of previous analytic and simple numerical calculations, we find a strong wave–field interaction, in which waves are reflected in the field region. The wave–field interaction and wave reflection depend on the field strength as well as on the adopted values of the diffusivities. In some cases, wave reflection leads to an increased mean flow in the field region. In addition to reproducing some of the features of our simpler models, we find additional complex behaviours in these more complete and realistic calculations. First, we find that the spectrum of wave generation, both in magnetized and in unmagnetized models, is not generally well described by available analytic models, although some overlap does exist. Similarly, we find that the dissipation of waves is only partially described by the results of linear theory. We find that the distortion of the field by waves and convective overshoot leads to rapid decay and entrainment of the magnetic field which subsequently changes the wave–field interaction. In addition, the field alters the amount of wave energy propagating into the deep radiative interior, at times increasing the wave energy there and at others decreasing it. Because of the complexity of the problem and because the durations of these simulations are shorter than the anticipated time-scale for dynamical adjustment of the deep solar interior, we are unable to draw a definitive conclusion regarding the efficiency of angular momentum transport in the deep radiative interior by IGW in the presence of a magnetic field.