Aims. Observations of shell-type supernova remnants (SNRs) in the GeV to multi-TeV -ray band, coupled with those at millimetre radio wavelengths, are motivated by the search for cosmic-ray accelerators in our Galaxy. The old-age mixed-morphology SNR W 28 (distance ∼2 kpc) is a prime target due to its interaction with molecular clouds along its northeastern boundary and other clouds situated nearby.Methods. We observed the W 28 field (for ∼40 h) at very high energy (VHE) -ray energies ( 0.1$]]> TeV) with the HESS. Cherenkov telescopes. A reanalysis of EGRET 100$]]> MeV data was also undertaken. Results from the NANTEN 4 m telescope Galactic plane survey and other CO observations were used to study molecular clouds. Results. We have discovered VHE -ray emission (HESS J1801-233) coincident with the northeastern boundary of W 28 and a complex of sources (HESS J1800-240A, B and C) ∼0.5° south of W 28 in the Galactic disc. The EGRET source (GRO J1801-2320) is centred on HESS J1801-233 but may also be related to HESS J1800-240 given the large EGRET point spread function. The VHE differential photon spectra are well fit by pure power laws with indices ∼2.3 to 2.7. The spectral indices of HESS J1800-240A, B, and C are consistent within statistical errors. All VHE sources are ∼10 in intrinsic radius except for HESS J1800-240C, which appears pointlike. The NANTEN CO() data reveal molecular clouds positionally associating with the VHE emission, spanning a ∼15 km s range in local standard of rest velocity. Conclusions. The VHE/molecular cloud association could indicate a hadronic origin for HESS J1801-233 and HESS J1800-240, and several cloud components in projection may contribute to the VHE emission. The clouds have components covering a broad velocity range encompassing the distance estimates for W 28 (∼2 kpc) and extending up to ∼4 kpc. Assuming hadronic origin and distances of 2 and 4 kpc for cloud components, the required cosmic-ray density enhancement factors (with respect to the solar value) are in the range ∼10 to ∼30. If situated at 2 kpc distance, such cosmic-ray densities may be supplied by SNRs like W 28. Additionally and/or alternatively, particle acceleration may come from several catalogued SNRs and SNR candidates, the energetic ultra compact HII region W 28A2, and the HII regions M 8 and M 20, along with their associated open clusters. Further sub-mm observations would be recommended to probe in detail the dynamics of the molecular clouds at velocites $]]> 10 km s and their possible connection to W 28.
- Gamma rays: observations