Context. HESS J1813–178 is a very-high-energy γ-ray source spatially coincident with the young and energetic pulsar PSR J1813–1749 and thought to be associated with its pulsar wind nebula (PWN). Recently, evidence for extended high-energy emission in the vicinity of the pulsar has been revealed in the Fermi Large Area Telescope (LAT) data. This motivates revisiting the HESS J1813–178 region, taking advantage of improved analysis methods and an extended dataset. Aims. Using data taken by the High Energy Stereoscopic System (H.E.S.S.) experiment and the Fermi-LAT, we aim to describe the γ-ray emission in the region with a consistent model, to provide insights into its origin. Methods. We performed a likelihood-based analysis on 32 hours of H.E.S.S. data and 12 yr of Fermi-LAT data and we fitted a spectro-morphological model to the combined datasets. These results allowed us to develop a physical model for the origin of the observed γ-ray emission in the region. Results. In addition to the compact very-high-energy γ-ray emission centred on the pulsar, we find a significant yet previously undetected component along the Galactic plane. With Fermi-LAT data, we confirm extended high-energy emission consistent with the position and elongation of the extended emission observed with H.E.S.S. These results establish a consistent description of the emission in the region from GeV energies to several tens of TeV. Conclusions. This study suggests that HESS J1813–178 is associated with a γ-ray PWN powered by PSR J1813–1749. A possible origin of the extended emission component is inverse Compton emission from electrons and positrons that have escaped the confines of the pulsar and form a halo around the PWN.