A search for neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) is performed using a data sample corresponding to an integrated luminosity of up to 13.3 fb$^{-1}$ from proton--proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS detector at the LHC. The heavy resonance is assumed to decay to a $\tau\tau$ pair with at least one $\tau$ lepton decaying hadronically. The search is performed in the mass range of 0.2-1.2 TeV. The data are in good agreement with the background predicted by the Standard Model, hence results are given as upper limits on the production cross section times branching fraction as a function of the Higgs boson mass. The results are interpreted in MSSM benchmark scenarios. The most stringent MSSM parameter space constraints from the search exclude at 95% confidence level $\tan\beta > 9$ for $m_A = 200$~\GeV\ and $\tan\beta > 50$ for $m_A = 1200$~\GeV\ in the $m_{h}^{\text{mod+}}$ MSSM scenario.

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