The interaction of Ni and Cu atoms as well as Ni-4 and Cu-4 clusters with cationic and anionic sites of the MgO(100) surface has been studied by means of gradient-corrected density functional calculations using cluster models. We found that the cationic surface atoms and the fourfold hollow sites are essentially inert while Ni and Cu atoms as well as their clusters are weakly oxidized by the surface oxygens. The adhesion energy is 0.62 eV/atom for Ni-4 and 0.36 eV/atom for Cu-4. This reflects the stronger bonding of a surface oxygen with a Ni atom, 1.24 eV, compared to a Cu atom, 0.28 eV. The reason for the stronger bonding of Ni is the presence of the uncomplete 3d shell. In fact, the mixing of the 3d orbitals with the O 2p band leads to the formation of a covalent polar bond of moderate strength. Cu binds mainly via the 4s electrons and the interaction is weaker. An important conclusion is that the metal-metal bonds in the cluster are stronger than the metal-substrate bonds. The adsorbed clusters feature somewhat longer intermetallic distances than in the gas phase, but clusters epitaxially adsorbed on top of the surface oxygens feature significantly longer metal-metal bonds and thus are less stable.