A search is performed for localized excesses in the low-mass dijet invariant mass distribution, targeting a hypothetical new particle decaying into two jets and produced in association with either a high transverse momentum photon or a jet. The search uses the full Run 2 data sample from LHC proton-proton collisions collected by the ATLAS experiment at a center-of-mass energy of 13 TeV during 2015-2018. Two variants of the search are presented for each type of initial-state radiation: one that makes no jet flavor requirements and one that requires both of the jets to have been identified as containing Formula Presented-hadrons. No excess is observed relative to the Standard Model prediction, and the data are used to set upper limits on the production cross section for a benchmark Formula Presented model and, separately, for generic, beyond the Standard Model scenarios which might produce a Gaussian-shaped contribution to dijet invariant mass distributions. The results extend the current constraints on dijet resonances to the mass range between 200 and 650 GeV.