The showdown between three federal judges and Gov. Jerry Brown over California’s overcrowded prison system is headed once again to the U.S. Supreme Court.

With the threat of contempt proceedings hanging over his administration, Brown and top prison officials on Friday reluctantly offered a plan to meet a court-ordered deadline for ending the state’s prison overcrowding crisis while at the same vowing to appeal to the Supreme Court. Jeff Beard, the state prisons chief, told this newspaper the state plans to move within nine days to push the case to the high court.

In a 46-page brief filed shortly before midnight Thursday, state officials outlined how they would reduce the prison population by about 10,000 inmates over the next year, hoping to satisfy a three-judge panel that last month blasted the governor for failing to comply with a 2009 order requiring California to reduce its prison population to about 110,000 by this summer.

“We think this is an ugly plan, and anything we do is going to cause some problems. We don’t think we should have to do that,” said Beard, secretary of the California Department of Corrections and Rehabilitation.

In the April order, the federal judges threatened the governor with contempt if he did not by Thursday devise a plan that would at least meet the cap by December. The judges previously found the state’s prisons are so far over capacity that they failed to provide adequate medical and mental health care for the nation’s largest prison population.

The administration’s response presented options, such as slowing the rate of return for inmates held in out-of-state prisons, leasing beds from larger county jails, increasing good-conduct credits for nonviolent inmates and housing more inmates at firefighting camps.

But state officials made it clear that all of the proposals, which would have to be approved by the Legislature, were undesirable, and rejected some of the suggestions from the three-judge panel, including the call to expand the governor’s realignment program. As a result, the state will present the plan to the Legislature “under protest,” as Beard put it Friday.

In court papers, the governor and prison leaders told the judges California has addressed concerns that its medical and mental health care for inmates fall below constitutional standards, spending billions of dollars to expand medical facilities and improve treatment.

Democratic lawmakers signaled that Brown’s plan may be dead on arrival in the Legislature, which the governor does not appear to mind. Senate President Pro Tem Darrell Steinberg said he supports Brown’s appeal to the Supreme Court, accusing the federal court of “ignoring the massive reform and reduction in prison population” over the past few years.

The state’s response is the latest twist in a legal standoff that pits California’s power to control its prisons against the federal courts’ ability to force a state prison system to correct problems that date back decades. The judges in 2009 ordered the state to reduce its inmate population to about 110,000 inmates at its 33 prisons, well below highs that have reached 160,000 in the past.

The Supreme Court upheld those orders in 2010, although in a sharply divided 5-4 decision. Legal experts say that close vote may indicate some justices would be receptive to Brown’s appeal, but predict the court may be reluctant to jump into the prison controversy again.

“Because it’s fact-specific and always evolving, I’d be surprised if they take it again,” said Doug Berman, an Ohio State University law professor.

But state officials now argue they’ve done enough to comply with constitutional standards, shedding more than 30,000 inmates, primarily through realignment, which has shifted many low-level offenders, such as probation violators, to county jails to relieve state prison overcrowding.

The federal judges found the prisons remain overstuffed, warning the state that “California still houses far more prisoners than its system is designed to house.”

However, the governor and prison officials argue that further steps could jeopardize public safety and cost the state hundreds of millions of dollars. The governor’s plan would cut the number of inmates by about 7,000 by the December deadline, still a few thousand short of the federal judges’ demands.

In court papers, the administration told the court that it would present the options to the Legislature, which would have to take emergency action to put any measures in place by a court-ordered December deadline to further reduce the prison population. But the governor made it clear it would do so without advocating actively for the solutions.

“The court’s ‘best efforts’ directive certainly cannot mean that the governor must advocate for the Legislature to pass measures that would jeopardize public safety,” the state said in court papers.

Lawyers for the inmates have accused the governor of defying the court orders and dragging his feet on the final steps needed to fix the state’s prison overcrowding problem.

Michael Bien, a lawyer for the inmates, said the governor and prison officials are trying to reopen issues they’ve “already lost,” rather than comply with the prison overcrowding orders.

“We’ve come a long way, yet there is more to do,” Bien said. “Instead of doing it, we’re at war.”

Howard Mintz covers legal affairs. Contact him at 408-286-0236 or follow him at Twitter.com/hmintz.