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Navigating animals continuously integrate velocity signals to update internal representations of their directional heading and spatial location in the environment. How neural circuits combine sensory and motor information to construct these velocity estimates and how these self-motion signals, in turn, update internal representations that support navigational computations are not well understood. Recent work in Drosophila has identified a neural circuit that performs angular path integration to compute the fly's head direction, but the nature of the velocity signal is unknown. Here we identify a pair of neurons necessary for angular path integration that encode the fly's rotational velocity with high accuracy using both visual optic flow and motor information. This estimate of rotational velocity does not rely on a moment-to-moment integration of sensory and motor information. Rather, when visual and motor signals are congruent, these neurons prioritize motor information over visual information, and when the two signals are in conflict, reciprocal inhibition selects either the motor or visual signal. Together, our results suggest that flies update their head direction representation by constructing an estimate of rotational velocity that relies primarily on motor information and only incorporates optic flow signals in specific sensorimotor contexts, such as when the motor signal is absent.