Detection of mosaic mutations that arise in normal development is challenging, as such mutations are typically present in only a minute fraction of cells and there is no clear matched control for removing germline variants and systematic artifacts. We present MosaicForecast, a machine-learning method that leverages read-based phasing and read-level features to accurately detect mosaic single-nucleotide variants and indels, achieving a multifold increase in specificity compared with existing algorithms. Using single-cell sequencing and targeted sequencing, we validated 80-90% of the mosaic single-nucleotide variants and 60-80% of indels detected in human brain whole-genome sequencing data. Our method should help elucidate the contribution of mosaic somatic mutations to the origin and development of disease.