Non-recurrent deep convolutional neural networks (DCNNs) are currently the best models of core object recognition; a behavior supported by the densely recurrent primate ventral stream, culminating in the inferior temporal (IT) cortex. Are these recurrent circuits critical to ventral stream's execution of this behavior? We reasoned that, if recurrence is critical, then primates should outperform feedforward-only DCNNs for some images, and that these images should require additional processing time beyond the feedforward IT response. Here we first used behavioral methods to discover hundreds of these "challenge" images. Second, using large-scale IT electrophysiology in animals performing core recognition tasks, we observed that behaviorally-sufficient, linearly-decodable object identity solutions emerged ~30ms (on average) later in IT for challenge images compared to DCNN and primate performance-matched "control" images. We observed these same late solutions even during passive viewing. Third, consistent with a failure of feedforward computations, the behaviorally-critical late-phase IT population response patterns evoked by the challenge images were poorly predicted by DCNN activations. Interestingly, deeper CNNs better predicted these late IT responses, suggesting a functional equivalence between recurrence and additional nonlinear transformations. Our results argue that automatically-evoked recurrent circuits are critical even for rapid object identification. By precisely comparing current DCNNs, primate behavior and IT population dynamics, we provide guidance for future recurrent model development.