Filtered backprojection (FBP) algorithms are commonly employed for image reconstruction in optoacoustic tomography (OAT). A limitation of FBP algorithms is that they require the measured acoustic data to be densely sampled, which necessitates expensive ultrasound arrays that possess a large number of elements or increased data-acquisition times if mechnical scanning is employed. Additionally, FBP algorithms are based on idealized imaging models that do not accurately model the response of the transducers and fail to exploit the statistical characteristics of noisy measurement data to minimize noise levels in the reconstructed images. Iterative image reconstruction algorithms can circumvent these difficulties. However, to date, iterative reconstruction algorithms have not been successfully applied to three-dimensional (3D) OAT. In this work we investigate the use of an iterative image reconstruction method in 3D OAT. The large computational burden of 3D iterative image reconstruction is circumvented by implementing the reconstrution algorithm with graphics processing units (GPUs). The ability of the reconstruction algorithm to mitigate artifacts due to incomplete data is demonstrated.