Interaural level differences (ILDs) are the dominant cue for localizing the sources of high frequency sounds that differ in azimuth. Neurons in the primary auditory cortex (A1) respond differentially to ILDs of simple stimuli such as tones and noise bands, but the extent to which this applies to complex natural sounds, such as vocalizations, is not known. In sufentanil/N2O anesthetized marmosets, we compared the responses of 76 A1 neurons to three vocalizations (Ock, Tsik, and Twitter) and pure tones at cells characteristic frequency. Each stimulus was presented with ILDs ranging from 20 dB favoring the contralateral ear to 20 dB favoring the ipsilateral ear to cover most of the frontal azimuthal space. The response to each stimulus was tested at three average binaural levels (ABLs). Most neurons were sensitive to ILDs of vocalizations and pure tones. For all stimuli, the majority of cells had monotonic ILD sensitivity functions favoring the contralateral ear, but we also observed ILD sensitivity functions that peaked near the midline and functions favoring the ipsilateral ear. Representation of ILD in A1 was better for pure tones and the Ock vocalization in comparison to the Tsik and Twitter calls; this was reflected by higher discrimination indices and greater modulation ranges. ILD sensitivity was heavily dependent on ABL: changes in ABL by +/-20 dB SPL from the optimal level for ILD sensitivity led to significant decreases in ILD sensitivity for all stimuli, although ILD sensitivity to pure tones and Ock calls was most robust to such ABL changes. Our results demonstrate differences in ILD coding for pure tones and vocalizations, showing that ILD sensitivity in A1 to complex sounds cannot be simply extrapolated from that to pure tones. They also show A1 neurons do not show level-invariant representation of ILD, suggesting that such a representation of auditory space is likely to require population coding, and further processing at subsequent hierarchical stages.