We give ab-initio data for the study of the stability of the atomic structures of Zr-rich ZrX (X = Sc-Cu) alloys, such as the cohesive energies and equilibrium Wigner-Seitz radii of elemental metals X (X = Sc-Cu, Zr-Ag) and X-X (X = Sc-Cu) interaction energies in Zr. The calculations are based on the density functional thoery in the generalized gradient approximation and employ the full-potential Korringa-Kohn-Rostoker Green's function method. Using the calculated results, we elucidate the fundamental features of interatomic interactions of Zr-rich ZrX alloys. Especially, we found that the pair interaction Of Cu impurities in Zr becomes strongly attractive around the interatomic distance of 0.45 similar to 0.46 nm. It is shown that this interaction may be important for the stability of icosahedron-like local atomic structures of Zr10Cu3 and Zr9Cu4 clusters in the Zr70Cu30 bulk metallic glass, being proposed experimentally. We also found that the atomic structure of an isolated Zr10X3 cluster transforms from the hcp structure (initial state) to an icosahedron-like structure (final state) for X = Cu, but not for X=Ni.