Letter-speech sound (LSS) integration is crucial for initial stages of reading acquisition. However, the relationship between cortical organization for supporting LSS integration, including unimodal and multimodal processes, and reading skills in early readers remains unclear. In the present study, we measured brain responses to Finnish letters and speech sounds from 29 typically developing Finnish children in a child-friendly audiovisual integration experiment using magnetoencephalography. Brain source activations in response to auditory, visual and audiovisual stimuli as well as audiovisual integration response were correlated with reading skills and cognitive skills predictive of reading development after controlling for the effect of age. Regression analysis showed that from the brain measures, the auditory late response around 400 ms showed the largest association with phonological processing and rapid automatized naming abilities. In addition, audiovisual integration effect was most pronounced in the left and right temporoparietal regions and the activities in several of these temporoparietal regions correlated with reading and writing skills. Our findings indicated the important role of temporoparietal regions in the early phase of learning to read and their unique contribution to reading skills.