Symbiotic X-ray binaries (SyXBs) are a recently discovered subclass of low mass X-ray binaries. Their growing number makes them an important evolutionary channel of X-ray binaries. Our goal is to perform spectral analysis and classification of the proposed counterparts to IGR J16358-4726 and IGR J16393-4643 and establish their nature as X-ray systems. We used the ESO/UT1 ISAAC spectrograph to observe the proposed counterparts to the two sources, obtaining K-band medium resolution spectra (R=500) with a S/N>140. Data reduction was performed with the standard procedure. We classified them by means of comparison with published atlases. We performed SED fitting to refine the spectral classification. The two counterparts clearly exhibit the typical features of late-type stars, notably strong CO absorption bands in the red part of the spectrum. With information from previous X-ray studies, we classify the two systems as two new members of the SyXB class. For IGR J16393-4643, we considered the most probable counterpart to the system, although three other objects cannot be completely discarded. For this system, we compared our findings with available orbital solutions, constraining the orbital parameters and the mass of the companion star. By including two more systems, we increased to eight the number of known SyXBs, which emerges as a non-negligible category of galactic X-ray binaries.