A search for new particles decaying into a pair of top quarks is performed using proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of s=13 TeV corresponding to an integrated luminosity of 36.1 fb-1. Events consistent with top-quark pair production and the fully hadronic decay mode of the top quarks are selected by requiring multiple high transverse momentum jets including those containing b-hadrons. Two analysis techniques, exploiting dedicated top-quark pair reconstruction in different kinematic regimes, are used to optimize the search sensitivity to new hypothetical particles over a wide mass range. The invariant mass distribution of the two reconstructed top-quark candidates is examined for resonant production of new particles with various spins and decay widths. No significant deviation from the Standard Model prediction is observed and limits are set on the production cross-section times branching fraction for new hypothetical Z′ bosons, dark-matter mediators, Kaluza-Klein gravitons and Kaluza-Klein gluons. By comparing with the predicted production cross sections, the Z′ boson in the topcolor-assisted-technicolor model is excluded for masses up to 3.1-3.6 TeV, the dark-matter mediators in a simplified framework are excluded in the mass ranges from 0.8 to 0.9 TeV and from 2.0 to 2.2 TeV, and the Kaluza-Klein gluon is excluded for masses up to 3.4 TeV, depending on the decay widths of the particles.