New particles with large masses that decay into hadronically interacting particles are predicted by many models of physics beyond the Standard Model. A search for a massive resonance that decays into pairs of dijet resonances is performed using 140 fb-1 of proton-proton collisions at s=13 TeV recorded by the ATLAS detector during Run 2 of the Large Hadron Collider. Resonances are searched for in the invariant mass of the tetrajet system, and in the average invariant mass of the pair of dijet systems. A data-driven background estimate is obtained by fitting the tetrajet and dijet invariant mass distributions with a four-parameter dijet function and a search for local excesses from resonant production of dijet pairs is performed. No significant excess of events beyond the Standard Model expectation is observed, and upper limits are set on the production cross sections of new physics scenarios.