Diffusion measurements on Li atoms adsorbed on a ruthenium single crystal were performed in the high-temperature regime, where desorption is an important path way in the atomic dynamics. Nuclear magnetic resonance (NMR) techniques were applied to highly nuclear spin-polarized Li-6 atoms adsorbed on a Ru(001) surface. Pulsed radio frequency (rf) fields with spatial gradients were used to create magnetization patterns in the lithium adsorbate which decay by atomic tracer diffusion. In the temperature range of 1100-1200 K, the diffusion coefficients were on the order of 0.1 cm(2)/s. The temperature dependence could be described by D = (10 +/- 7 cm(2)/s) exp[-(0.46 +/- 0.07 eV)/(kT)]. The very large prefactor can be explained by a mean jump length on the order of 200 Angstrom. This means the adsorbate is in a gaslike state on the surface, where localization occurs at sites far apart from each other. In a spin-echo experiment at a surface temperature of 1150 K, the spin-spin relaxation time was determined to T-2 = 81 +/- 8 ms.