Precise genome-editing technologies such as base editing1,2 and prime editing3 can correct most pathogenic gene variants, but their widespread clinical application is impeded by the need to develop new therapeutic agents for each mutation. For diseases that are caused by premature stop codons, suppressor tRNAs (sup-tRNAs) offer a more general strategy. Existing approaches to use sup-tRNAs therapeutically, however, require lifelong administration4,5 or show modest potency, necessitating potentially toxic overexpression. Here we present prime editing-mediated readthrough of premature termination codons (PERT), a strategy to rescue nonsense mutations in a disease-agnostic manner by using prime editing to permanently convert a dispensable endogenous tRNA into an optimized sup-tRNA. Iterative screening of thousands of variants of all 418 human tRNAs identified tRNAs with the strongest sup-tRNA potential. We optimized prime editing agents to install an engineered sup-tRNA at a single genomic locus without overexpression and observed efficient readthrough of premature termination codons and protein rescue in human cell models of Batten disease, Tay-Sachs disease and cystic fibrosis. In vivo delivery of a single prime editor that converts an endogenous mouse tRNA into a sup-tRNA extensively rescued disease pathology in a model of Hurler syndrome. PERT did not induce detected readthrough of natural stop codons or cause significant transcriptomic or proteomic changes. Our findings suggest the potential of disease-agnostic therapeutic genome-editing approaches that require only a single composition of matter to treat diverse genetic diseases.