15 pages, 6 figures, 3 tablesThe gamma-ray pulsar PSR B1706-44 and the adjacent supernova remnant (SNR) candidate G343.1-2.3 were observed by H.E.S.S. during a dedicated observation campaign in 2007. As a result of this observation campaign, a new source of very-high-energy (VHE; E > 100 GeV) gamma-ray emission, HESS J1708-443, was detected with a statistical significance of 7 sigma, although no significant point-like emission was detected at the position of the energetic pulsar itself. In this paper, the morphological and spectral analyses of the newly-discovered TeV source are presented. The centroid of HESS J1708-443 is considerably offset from the pulsar and located near the apparent center of the SNR, at RA(J2000) = 17h08m11s +/- 17s a...