Na clusters bound to mica surfaces have been irradiated with pulsed and cw visible laser light. Kinetic energy and angular distributions of the Na atoms desorbing from the dusters have been determined using cw two-photon laser-induced fluorescence detection. In addition the dependence of the desorption rate on laser power, wavelength and polarization has been measured. The most probable kinetic energy E(kin) of the photodesorbed atoms at the surface temperature T-s=300 K was found to be E(kin)=18+/-5 meV, independent of laser irradiance (3 mu J/cm(2)...20 mJ/cm(2)) and wavelength (450 nm, 505 nm, 658 nm). With increasing orientation angle between detection axis and surface normal (0 degrees less than or equal to Theta less than or equal to 90 degrees) E(kin) was observed to decrease slightly, while it was nearly independent of surface temperature between T-s=30 K and T-s=300 K. Also, with increasing radius of the Na clusters the desorbing Na atoms slowed down. The angular distribution of the Na atoms was of cos(2)-type with respect to the surface normal. These observations suggest that laser-induced desorption of Na from Na clusters bound to mica surfaces involves an initial rate-limiting step of direct surface plasmon excitation followed by a final step of delayed thermal desorption.