Water molecules adsorbed on the CeO(2)(111) surface are investigated by non-contact atomic force microscopy (NC-AFM) at several tip-sample temperatures ranging between 10 and 300 K. Depending on the strength of the tip-surface interaction, they appear as triangular protrusions extended over three surface oxygen atoms or as small pits at hollow sites. During NC-AFM imaging with the tip being close to the surface, occasionally the transfer of molecules between tip and surface or the tip-induced lateral displacement of water molecules to equivalent surface lattice sites is observed. We report how this situation can be exploited to produce controlled lateral manipulations. A protocol to manipulate the water molecules between pre-defined neighbouring equivalent adsorption sites of the regular lattice as well as across a surface oxygen vacancy is demonstrated.