The adsorption geometry, binding energy and electronic structure of alkali metal overlayers on the MgO (001) surface have been studied by means of density functional theory, using Gaussian-type orbitals to expand the wave functions and electronic charge density. A two-dimensionally periodic slab of MgO with alkali metal adsorbed at one surface was used to model the semi-infinite system. Li, Na, and K were considered at both half- and quarter-monolayer coverage. Results were compared for the local density approximation and for two different forms of the generalized gradient approximation. In all cases Li was found to interact with the surface approximately twice as strongly as Na and three times as strongly as K. The epitaxial binding energies were, however, always less than or close to the bulk cohesive energies of the respective alkali metals, suggesting an instability of the adsorbed film toward the formation of two- or three-dimensional islands, in agreement with experiment. Spin polarized and unpolarized calculations were compared to detect metal-insulator transitions in the alkali overlayer. Only Li adsorbed at 1:4 coverage was found to have lower energy in a spin polarized (hence nonmetallic) state.