Gravitational instability (GI) features in several aspects of protostellar disc evolution, most notably in angular momentum transport, fragmentation, and the outbursts exemplified by FU Ori and EX Lupi systems. The outer regions of protostellar discs may also be coupled to magnetic fields, which could then modify the development of GI. To understand the basic elements of their interaction, we perform local 2D ideal and resistive magnetohydrodynamics simulations with an imposed toroidal field. In the regime of moderate plasma beta, we find that the system supports a hot gravitoturbulent state, characterized by considerable magnetic energy and stress and a surprisingly large Toomre parameter Q ≳ 10. This result has potential implications for disc structure, vertical thickness, ionization, etc. Our simulations also reveal the existence of long-lived and dense ‘magnetic islands’ or plasmoids. Lastly, we find that the presence of a magnetic field has little impact on the fragmentation criterion of the disc. Though our focus is on protostellar discs, some of our results may be relevant for the outer radii of AGN.