Ab initio density-functional theory has been used to investigate the adsorption of NH3 molecules on Ag(111), (001), and (110) surfaces. Preferred adsorption sites, adsorption energies, and the relaxation of the surface structure were calculated using the all-electron full-potential linearized augmented plane wave method. We find that NH3 binds preferentially at a top site with the C-3 axis normal to the surface. At this site, the N-Ag distance is practically the same for every surface, while the adsorption energy depends on the surface structure: 0.32, 0.40, and 0.49 eV per molecule for (111), (001), and (110), respectively. Additionally, the electronic structure and binding energies of NH3Agn (n=1,2) complexes have been calculated to investigate to what extent the formation of the weak N-Ag chemical bond might be determined mainly by local interactions. The bonding mechanism is explained as resulting from the combined effects of covalent and polarization contributions.