In auditory cortex, neural responses to stimuli inside receptive fields (RFs) can be further facilitated by behavioral demands, such as attending to a spatial location. It is less clear how off-RF stimuli modulate neural responses and contribute to behavioral tasks. Our recent study revealed a particular form of location-specific facilitation evoked by repeated stimulation from an off-RF location, suggesting behavioral modulation of spatial RFs. To further explore this question, we trained marmosets to attend to sound locations that were either inside or outside the RFs of auditory cortical neurons. The majority of neurons showed increased firing rates at target locations inside their RFs. Interestingly, this increase also occurred outside the RFs, sometimes exceeding the responses at the RF center during passive listening. These task-related off-RF facilitation were much more common in the caudal area than in the rostral area and the primary auditory cortex. A normalization model reproduced the off-RF facilitation using widespread suppression. The model's prediction was confirmed by experimental observations of widespread reductions in firing rate and hyperpolarized membrane potentials for off-RF stimuli. These results suggest that behavioral task demands recruit a broader range of neurons than those that are responsive to a target sound in the passive state.