We investigate optical properties of the Kretschmann setup, which contains a dielectric prism and a metal layer and may also contain an additional dielectric layer. We show that the investigated structure allows one to generate a transverse-magnetic- (TM-) polarized spatiotemporal optical pulse comprising an optical vortex using the “conventional” Kretschmann configuration without an additional layer. We also demonstrate that in the case of transverse electric (TE) polarization, the additional dielectric layer is necessary for satisfying the optical vortex generation condition. The results of rigorous numerical simulations demonstrate the possibility of generating spatiotemporal optical vortices with high quality for both TM- and TE-polarizations.