We present deep L- (3.8 μm) and M- (4.7 μm) band imaging with the Infrared Spectrometer and Array Camera (ISAAC) on the ESO Very Large Telescope (VLT) with unprecedented spatial resolution of the nearby Seyfert 2 galaxies NGC 7496 and NGC 7582 and the Seyfert 1 galaxy NGC 7213, all at a comparable distance. The unresolved nuclear component dominates the emission within the central 90 pc region, while the host galaxy accounts for up to 50% of the integrated emission at both wavelengths within the detected sizes of ~1 kpc in the L band and ~0.5 kpc in the M band. The overall morphology of the extended component follows the general isophote pattern defined by the near-infrared continuum of the galaxies. However, the central 300 pc regions show much more ordered elliptical isophotes than in the near-infrared. In particular, emission in the L and M bands shows well-defined central point sources in the two Seyfert 2 galaxies. The brightness of the Seyfert nuclei in the LM bands indicates that the Seyfert 2 galaxy NGC 7582 harbors as powerful a nucleus as that in the Seyfert 1 galaxy NGC 7213, while the Seyfert 2 galaxy NGC 7496 is intrinsically weaker. In NGC 7582, we have detected the circumnuclear star-forming ring in the L band.