Searches for high-mass resonances in the dijet invariant mass spectrum with one or two jets identified as b -jets are performed using an integrated luminosity of 3.2 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. No evidence of anomalous phenomena is observed in the data, which are used to exclude, at 95% credibility level, excited b⁎ quarks with masses from 1.1 TeV to 2.1 TeV and leptophobic Z′ bosons with masses from 1.1 TeV to 1.5 TeV. Contributions of a Gaussian signal shape with effective cross sections ranging from approximately 0.4 to 0.001 pb are also excluded in the mass range 1.5–5.0 TeV.