WASHINGTON — Attorney General William P. Barr ordered the Bureau of Prisons on Friday to expand the group of federal inmates eligible for early release and to prioritize those at three facilities where known coronavirus cases have grown precipitously, as the virus threatens to overwhelm prison medical facilities and nearby hospitals.

Mr. Barr wrote in a memo to Michael Carvajal, the director of the Bureau of Prisons, that he was intensifying the push to release prisoners to home confinement because “emergency conditions” created by the coronavirus have affected the ability of the bureau to function.

He directed the bureau to prioritize the release of prisoners from federal correctional institutions in Louisiana, Connecticut and Ohio, which comprise the bulk of the system’s 91 inmates and 50 staff members who have tested positive for the coronavirus.

At least five inmates have died at the federal prison in Oakdale, La., and two have died at the federal prison near Elkton, Ohio. Officials with unions that represent prison workers have said that the reported numbers are likely undercounting the number of infected staff, given the paucity of testing.