We present the results of a narrow-band infrared imaging survey of a narrow strip (12' wide) around the Galactic equator between 6° and 21° of galactic longitude aimed at detecting field stars with strong CO absorption, mainly late-type giants and supergiants. Our observations include follow-up low resolution spectroscopy (R=980) of 191 selected candidates in the H and K bands. Most of these objects have photometric and spectroscopic characteristics consistent with their being red giants, and some display broad, strong absorption wings due to water vapor absorption between the H and K bands. We also identify in our sample 18 good supergiant candidates characterized by their lack of noticeable water absorption, strong CO bands in the H and K windows, and HKS photometry suggestive of high intrinsic luminosity and extinction reaching up to AV≃40mag. Another 9 candidates share the same features except for weak H2O absorption, which is also observed among some M supergiants in the solar neighbourhood. Interesting differences are noticed when comparing our stars with a local sample of late-type giants and supergiants, as well as with a sample of red giants in globular clusters of moderately subsolar metallicity and to a sample of bulge stars. A large fraction of the stars in our sample have CaI and NaI features markedly stronger than those typical in the local reference sample (both giants and supergiants), whereas the equivalent widths of the CO bands are similar or weaker. In this regard, our stars in the inner Milky Way disk display differences very similar to those identified by other authors between cool giants and supergiants near the galactic center and their counterparts in the solar neighbourhood. We propose that the systematic spectroscopic differences of our inner Galaxy stars are due to their higher metallicities that cause deeper mixing in their mantles, resulting in lower surface abundances of C and O and higher abundances of CN, which contribute to the strength of the CaI and NaI features at low resolution. Our results stress the limitations of using local stars as templates for the study of composite cool stellar populations such as central starbursts in galaxies.