Pedro Barrientos, 74, is accused of killing the popular Chilean singer in 1973. In a civil case, Mr. Barrientos was accused of bragging about shooting Mr. Jara twice in the head.
Immigrant advocacy groups say they will sue the agency if it fails to release the findings of an investigation into Melvin Ariel Calero Mendoza's death.
Undocumented immigrants accused of minor crimes are often sent back to their homelands. Danelo Cavalcante, who escaped from a U.S. prison, had been facing a murder charge in Brazil.
The roughly 91,000 migrants who were arrested after crossing together as families exceeded a record set in May 2019, the height of the border crisis during the Trump administration.