The efficiency of homology-directed repair (HDR) plays a crucial role in the development of animal models and gene therapy. We demonstrate that microhomology-mediated end-joining (MMEJ) constitutes a substantial proportion of DNA repair during CRISPR-mediated gene editing. Using CasRx to downregulate a key MMEJ factor, Polymerase Q (Polq), we improve the targeted integration efficiency of linearized DNA fragments and single-strand oligonucleotides (ssODN) in mouse embryos and offspring. CasRX-assisted targeted integration (CATI) also leads to substantial improvements in HDR efficiency during the CRISPR/Cas9 editing of monkey embryos. We present a promising tool for generating monkey models and developing gene therapies for clinical trials.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13059-023-02987-w.