HESS J1809-193 is an unidentified TeV source discovered by the High Energy Stereoscopic System and originally classified as a pulsar wind nebula (PWN) candidate associated with the pulsar PSR J1809-1917. However, a recent study of deep radio observations and the interstellar medium near the source has found evidence for a hadronic scenario for the gamma-rays. Here, a detailed study of the GeV emission in the region using data from the Fermi-LAT is presented. The GeV emission has an extended morphology in the region of the TeV emission and the overall spectrum can be accounted for by a cosmic-ray population having a simple power-law spectrum with energies extending up to 1 PeV. However, the spectrum at tens of TeV should be observed more deeply in the future to confirm its hadronic nature, and other scenarios involving combinations of leptonic and hadronic emission from several of the known supernova remnants in the region cannot be ruled out. The nearby TeV source HESS J1813-178, thought to be a PWN, is also studied in detail at GeV energies and we find a region of significant emission that is much more extended than the TeV emission and whose spectrum is softer than expected from a PWN but similar to those seen in several star-forming regions that are believed to accelerate protons. There is marginal evidence for a GeV point source at the location of the X-ray PWN, beside the extended emission.