Pol III core is the three‐subunit subassembly of the E. coli replicative DNA polymerase III holoenzyme. It contains the catalytic polymerase subunit α, the 3′ → 5′ proofreading exonuclease ε, and a subunit of unknown function, θ. We employ optical tweezers to characterize pol III core activity on a single DNA substrate. We observe polymerization at applied template forces F < 25 pN and exonucleolysis at F > 30 pN. Both polymerization and exonucleolysis occur as a series of short bursts separated by pauses. For polymerization, the initiation rate after pausing is independent of force. In contrast, the exonucleolysis initiation rate depends strongly on force. The measured force and concentration dependence of exonucleolysis initiation fits well to a two‐step reaction scheme in which pol III core binds bimolecularly to the primer‐template junction, then converts at rate k
2 into an exo‐competent conformation. Fits to the force dependence of k
init show that exo initiation requires fluctuational opening of two base pairs, in agreement with temperature‐ and mismatch‐dependent bulk biochemical assays. Taken together, our results support a model in which the pol and exo activities of pol III core are effectively independent, and in which recognition of the 3′ end of the primer by either α or ε is governed by the primer stability. Thus, binding to an unstable primer is the primary mechanism for mismatch recognition during proofreading, rather than an alternative model of duplex defect recognition.