We report early follow-up observations of the error box of the short burst GRB 050813 using the telescopes at Calar Alto and Observatorio Sierra Nevada, followed by deep VLT FORS2 I-band observations obtained under very good seeing conditions 5.7 and 11.7 days after the event. Neither a fading afterglow nor a rising SN component was found, so the potential GRB host galaxy has not been identified based on a comparison of the two VLT images taken at different epochs. We discuss whether any of the galaxies present in the original 10″ XRT error circle could be the host. In any case, the optical afterglow of GRB 050813 was of very low luminosity. We conclude that all these properties are consistent with the binary compact merger hypothesis for the progenitor of GRB 050813. Based on observations collected at the European Southern Observatory, La Silla, and Paranal, Chile (ESO Program 075.D-0415), and on observations taken at the German-Spanish Calar Alto Observatory and at IAA's Observatorio de Sierra Nevada in Spain.