Using the full-potential linearized augmented plane wave (FP-LAPW) density functional approach we have studied the electronic and structural characteristics of free and palladium-supported MgO(100) thin films. For the unsupported MgO films we found a non-negligible reduction of the in-plane lattice parameters together with an expansion of the interlayer distances. The electronic structure is driven mainly by the thickness-induced gap reduction, compensated to a large extent by the gap opening due to the reduction of the interatomic distances. When a pseudomorphic MgO(100) monolayer is deposited on the Pd(100) surface, the palladium-oxygen interaction induces partially filled antibonding oxygen states at the Fermi level, showing a possible weak, substrate-induced, conductor behavior of the MgO layer, and resulting in a considerable reduction of its work function. Furthermore, we show that the properties of an oxygen vacancy in the supported MgO monolayer differ substantially from those of the perfect MgO(100) surface. In particular, one of the two electrons trapped in the vacancy is transferred to the metallic substrate. The characteristics of the perfect MgO(100) surface and of the corresponding oxygen vacancy are recovered for a two-layer film.