This Letter describes a model-agnostic search for pairs of jets (dijets) produced by resonant and non-resonant phenomena beyond the Standard Model in 3.6 fb-1 of proton-proton collisions with a centre-of-mass energy of s=13 TeV recorded by the ATLAS detector at the Large Hadron Collider. The distribution of the invariant mass of the two leading jets is examined for local excesses above a data-derived estimate of the smoothly falling prediction of the Standard Model. The data are also compared to a Monte Carlo simulation of Standard Model angular distributions derived from the rapidity of the two jets. No evidence of anomalous phenomena is observed in the data, which are used to exclude, at 95% CL, quantum black holes with threshold masses b...