A search for neutral Higgs bosons of the minimal supersymmetric standard model (MSSM) and for a heavneutral Z′ boson is performed using a data sample corresponding to an integrated luminosity of 3.2 fb -1 from proton–proton collisions at s=13 TeV recorded by the ATLAS detector at the LHC. The heavy resonance is assumed to decay to a τ+τ- pair with at least one τ lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2–1.2 TeV for the MSSM neutral Higgs bosons and 0.5–2.5 TeV for the heavy neutral Z′ boson. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in MSSM and Z′ benchmark scenarios. The most stringent constraints on the MSSM mA – tanβ space exclude at 95 % confidence level (CL) tanβ>7.6 for mA=200 GeV in the mhmod+ MSSM scenario. For the Sequential Standard Model, a ZSSM′ mass up to 1.90 TeV is excluded at 95 % CL and masses up to 1.82–2.17 TeV are excluded for a ZSFM′ of the strong flavour model.