Using the modified embedded atom model in conjunction with a self-consistent tight-binding method, we calculated the structures and magnetic properties of small Fe-n clusters (n=2-9) supported on the Ni(001) surface. The structures are predicted to be two-dimensional islands, and the average spin magnetic moment per d hole is found hardly to vary with n. This latter finding contrasts with conclusions recently drawn on the basis of x-ray magnetic circular dichroism results. The magnetic moments of the individual Fe atoms in each cluster tended to increase with decreasing coordination number, and noncollinear tight-binding calculations showed all systems to be ferromagnetic. Cluster magnetism was hardly affected by Fe-Ni hybridization.