Against growing odds, Gov. Jerry Brown formally asked the U.S. Supreme Court late Friday to intervene once again in California's yearslong battle with federal judges over control of the state's prison system.

The Democratic governor filed his formal appeal asking the justices to overturn a lower court decision requiring the state to reduce its prison population by nearly 10,000 inmates by the end of the year to improve conditions.

The appeal came the same day as the U.S. Justice Department indicated that it may intervene in an ongoing lawsuit over California's treatment of inmates with severe mental illness, and as a lower federal court dumped cold water on the administration's plan to transfer more inmates to private prisons in other states.

Brown filed the appeal just a week after the Supreme Court soundly rejected the state's request to postpone the lower court's requirement that California reduce what once was the nation's largest correctional system to hold no more than 110,000 inmates in its major prisons.