A comparative study of atomic chemisorption at a metal surface is performed using free- and embedded-cluster models. A newly developed implementation of the moderately-large embedded-cluster (MLEC) approach is employed to describe the coupling of a surface cluster to its crystalline environment modelled by a slab. All calculations are done in the framework of density-functional theory using the local-density approximation. The cluster calculations are performed with the accurate all-electron linear-combination-of-Gaussian-type-orbitals formalism. The electronic structure of the substrate slab model is described using a linear-combination-of-Slater-type-orbitals method. A modification of the original MLEC formalism allows its application to metal substrates. The method is used here for the first time in combination with a 'first-principles' calculational scheme for the optimization of adsorption geometries employing an extended multilayered substrate. For the examples of H and O adsorption on the Li(001) surface clusters of different sizes are examined to explore the effects of embedding and the range of applicability of the MLEC method. The most pronounced effects observed are related to the charge rearrangement induced by adsorption. It is demonstrated that embedded clusters mirror the surface polarization of the Li(001) substrate and that the unphysical polarizability of free-cluster models is quenched due to embedding.