Focused pulse-laser-induced propagating magnetostatic surface spin waves (MSSWs) were investigated using an all-optical space-time-resolved magneto-optical Kerr effect microscope in 20-nm-thick permalloy thin films to clarify reciprocity and symmetry of MSSW emission. The microscope setup was constructed with variable direction of the applied magnetic field, and the corresponding angular dependence was examined. MSSWs were reciprocally emitted from the laser spot, in contrast to the nonreciprocal emission obtained by the antenna method. Specifically, the observed excitation amplitude and phase were independent of the propagation and magnetization directions within experimental error. By transforming the data into wave number-frequency space, the MSSW dispersion relation was clearly identified within the wave number of 2-3 rad/μm and frequency of 10 GHz. These observations are consistent with the model of ultrafast modulation of out-of-plane shape magnetic anisotropy inside the focused laser spot. In addition to confirming the symmetric and reciprocal emission of laser-induced MSSWs, the study demonstrated that this technique can provide all-optical microscopic spectroscopy for MSSW in metals, such as Brillouin light-scattering technique.