A search for heavy neutral Higgs bosons and Z′ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb−1 from proton-proton collisions at s=13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to τ+τ− with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for Z′ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude tan β > 1.0 for mA = 0.25 TeV and tan β > 42 for mA = 1.5 TeV at the 95% confidence level. For the Sequential Standard Model, ZSSM′ with mZ′ < 2.42 TeV is excluded at 95% confidence level, while ZNU′ with mZ ′ < 2.25 TeV is excluded for the non-universal G(221) model that exhibits enhanced couplings to third-generation fermions.