Context : Aims : The main goal of this paper is to provide new insights on the origin of the observable flux of \gamma rays from HESS J1809 - 193 using new high-quality observations in the radio domain . Methods : We used the Expanded Very Large Array ( now known as the Karl G. Jansky Very large Array , JVLA ) to produce a deep full-synthesis imaging at 1.4 GHz of the vicinity of PSR J1809 - 1917 . These data were used in conjunction with ^ { 12 } CO observations from the James Clerk Maxwell Telescope in the transition line J= 3 - 2 and atomic hydrogen data from the Southern Galactic Plane Survey to investigate the properties of the interstellar medium in the direction of the source HESS J1809 - 193 . Results : The new radio continuum image , obtained with a synthesized beam of 8 ^ { \prime \prime } \times 4 ^ { \prime \prime } and a sensitivity of 0.17 mJy beam ^ { -1 } , reveals with unprecedented detail all the intensity structures in the field . No radio counterpart to the observed X-ray emission supposed to be a pulsar wind nebula powered by PSR J1809 - 1917 is seen in the new JVLA image . We discovered a system of molecular clouds on the edge of the supernova remnant ( SNR ) G11.0 - 0.0 shock front , which is positionally coincident with the brightest part of the TeV source HESS J1809 - 193 . We determine , on the basis of kinematic and morphological evidences , a physical link of the SNR with the clouds for which we estimated a total ( molecular plus atomic ) mass of \sim 3 \times 10 ^ { 3 } M _ { \odot } and a total proton density in the range 2-3 \times 10 ^ { 3 } cm ^ { -3 } . Conclusions : We propose as the most likely origin of the very high-energy \gamma -ray radiation from HESS J1809 - 193 a hadronic mechanism through collisions of ions accelerated at the SNR G11.0 - 0.0 shock with the molecular matter in the vicinity of the remnant .