Dijet events are studied in the proton-proton collision data set recorded at s=13 TeV with the ATLAS detector at the Large Hadron Collider in 2015 and 2016, corresponding to integrated luminosities of 3.5 fb-1 and 33.5 fb-1 respectively. Invariant mass and angular distributions are compared to background predictions and no significant deviation is observed. For resonance searches, a new method for fitting the background component of the invariant mass distribution is employed. The data set is then used to set upper limits at a 95% confidence level on a range of new physics scenarios. Excited quarks with masses below 6.0 TeV are excluded, and limits are set on quantum black holes, heavy W′ bosons, W∗ bosons, and a range of masses and couplin...