Under difficult viewing conditions, the brain’s visual system uses a variety of recurrent modulatory mechanisms to augment feedforward processing. One resulting phenomenon is contour integration, which occurs in the primary visual (V1) cortex and strengthens neural responses to edges if they belong to a larger smooth contour. Computational models have contributed to an understanding of the circuit mechanisms of contour integration, but less is known about its role in visual perception. To address this gap, we embedded a biologically grounded model of contour integration in a task-driven artificial neural network and trained it using a gradient-descent variant. We used this model to explore how brain-like contour integration may be optimized for high-level visual objectives as well as its potential roles in perception. When the model was trained to detect contours in a background of random edges, a task commonly used to examine contour integration in the brain, it closely mirrored the brain in terms of behavior, neural responses, and lateral connection patterns. When trained on natural images, the model enhanced weaker contours and distinguished whether two points lay on the same versus different contours. The model learned robust features that generalized well to out-of-training-distribution stimuli. Surprisingly, and in contrast with the synthetic task, a parameter-matched control network without recurrence performed the same as or better than the model on the natural-image tasks. Thus, a contour integration mechanism is not essential to perform these more naturalistic contour-related tasks. Finally, the best performance in all tasks was achieved by a modified contour integration model that did not distinguish between excitatory and inhibitory neurons.