We report molecular dynamics (MD) computer simulations of a single lithium or iodide ion near a water\liquid mercury interface. The ion-mercury and the water-mercury potentials are derived from ab initio calculations of an ion or a water molecule and a mercury cluster consisting of seven, nine or 10 atoms. The flexible BJH water model and a mercury-mercury potential derived from pseudopotential theory are employed. The ion-water potentials are also based on ab initio calculations. The structural properties at the interfaces are described in terms of various density profiles and the ion-mercury radial distribution functions (RDF). An analysis of the induced rearrangements of the mercury atoms at and below the surface is also performed. Finally, the spectral densities of the hindered translational motions of the ions parallel and perpendicular to the mercury surface are reported. We conclude that, while the I--ion is contact adsorbed on the mercury surface, the Li+-ion is not.