In the present work, we spatially extended a brand new kinetic mechanism of the NO + NH3 reaction on Pt{100} to simulate the experimentally observed spatiotemporal traveling waves. The kinetic mechanism developed by Irurzun, Mola, and Imbihl (IMI model) improves the former model developed by Lombardo, Fink, and Imbihl (LFI model) by replacing several elementary steps to take into account experimental evidence published since the LFI model appeared. The IMI model achieves a better agreement with the experimentally observed dependence of the oscillation period on temperature. In the present work, the IMI model is extended by considering Fickean diffusion and coupling via the gas phase. Traveling waves propagating across the surface are obtained at realistic values of temperature and partial pressure. A transition from amplitude to phase waves is observed, induced either by temperature or by the gas global coupling strength. The traveling waves simulated in the present work are not associated with fixed defects, in agreement with experimental evidence of spiral centers capable of moving on the surface. Also, the IMI model adequately predicts the presence of macroscopic oscillations in the partial pressures of the reactants coexisting with front wave patterns on the surface.