Despite consensus on the neurological nature of autism spectrum disorders (ASD), brain biomarkers remain unknown and diagnosis continues to be based on behavioral criteria. Growing evidence suggests that brain abnormalities in ASD occur at the level of interconnected networks; however, previous attempts using functional connectivity data for diagnostic classification have reached only moderate accuracy. We selected 252 low-motion resting-state functional MRI (rs-fMRI) scans from the Autism Brain Imaging Data Exchange (ABIDE) including typically developing (TD) and ASD participants (n=126 each), matched for age, non-verbal IQ, and head motion. A matrix of functional connectivities between 220 functionally defined regions of interest was used for diagnostic classification, implementing several machine learning tools. While support vector machines in combination with particle swarm optimization and recursive feature elimination performed modestly (with accuracies for validation data sets <70%), diagnostic classification reached high accuracy of 91% with random forest (RF), a nonparametric ensemble learning method. Among the 100 most informative features (connectivities), for which this peak accuracy was achieved, participation of somatosensory, default mode, visual, and subcortical regions stood out. Whereas these findings were in part not unexpected, given previous findings of default mode abnormalities and atypical visual functioning in ASD, the prominent role of somatosensory regions was remarkable. The finding of peak accuracy for 100 interregional functional connectivities further suggests that brain biomarkers of ASD may be regionally complex and distributed, rather than localized.