U.S. prosecutors accused Honduran President Juan Orlando Hernández of conspiring with his brother and other top politicians to protect drug traffickers.

The allegations from federal prosecutors in New York were included in a lengthy court document released Friday that provides details of their case against President Hernández’s younger brother, Juan Antonio “Tony” Hernández, a former Honduran lawmaker. The younger Mr. Hernández is described by prosecutors as “a violent, multi-ton drug trafficker” who stamped his initials on...