We report the results of nonrelativistic and relativistic gradient-corrected density functional calculations on the interaction of single transition metal atoms with the oxygen sites of the regular MgO(001) surface. The surface has been represented by stoichiometric clusters of ions embedded in large arrays of point charges. Two adsorption sites have been considered, the on-top adsorption on the oxide anion and the bridge adsorption over two adjacent oxide anions; on-top adsorption is found to be energetically preferred. The metal atoms considered are Cr, Mo, W; Ni, Pd, Pt; Cu, Ag, and Au. These adsorbates can be classified into two groups depending on the strength of the bond with the surface. Cu, Ag, Au, Cr, and Mo exhibit weak or very weak bonds of the order of one-third of an electronvolt; their interaction is due to polarization and dispersion with Little mixing with the substrate orbitals. Ni, Pd, Pt, and W, on the other hand, form relatively strong bonds, of the order of 1 eV, with the oxide anions. This bond has a covalent polar nature with little charge transfer from the metal to the oxide. This is consistent with the fact that MgO is a wide gap insulator with very weak oxidizing power. The consequences of the different bonding mechanisms for the growth of metal particles on this oxide surface are discussed.