The cap was ordered by three federal judges in California, and Brown had asked the high court to remove it. Having lost that bid, he will continue to pursue a request to the lower court for more time to comply, according to a California Department of Corrections and Rehabilitation spokeswoman.
The Supreme Court justices said they found no grounds to take up the population limit, dispatching the governor's request in a single sentence: "The appeal is dismissed for want of jurisdiction."
Brown had no immediate response to the decision. A spokeswoman in his corrections department, Deborah Hoffman, issued a statement saying that the administration was "disappointed."
While awaiting the Supreme Court's decision, the governor recently asked the three-judge panel to give him three years to lower inmate numbers for the long term by, for example, expanding rehabilitation programs that could help keep offenders from returning to prison once they leave.
The court gave the state an extra month instead, until Jan. 27, and ordered officials to conduct settlement talks with lawyers for the inmates whose lawsuits led to the population cap. A report on those mediation efforts is due next week.
Brown and lawmakers approved funding in September for the rehabilitation programs, and the governor has touted "historic reforms" that have already been made — such as a new law requiring reconsideration of some sentences — that need time to work.
"California will continue to build on these landmark reforms with our law enforcement and local government partners," Hoffman said Tuesday.
If the settlement talks do not yield a result that is acceptable to the court, Brown could be left with more difficult options: Spend hundreds of millions of dollars to rent privately owned prison beds or concede to major changes in whom California incarcerates.
The governor so far has fought proposals to shorten the sentences of inmates who are considered at low risk to re-offend, saying that would threaten public safety. He has vowed to keep prisoners locked up, sending them to private facilities across the country if necessary.
But the judges have temporarily barred him from moving more prisoners out of state.
"I'm among those who think there are no easy solutions," said Michael Romano, director of the Three Strikes Project at Stanford University.
Romano said thousands of inmates could leave the system relatively quickly if local courts speed up reviews of sentences in about 2,000 pending three-strikes cases. Californians voted last year to ease the state's three-strikes law and apply its new standards retroactively.
The judges ordered that the mediation discussions include three-strikes prisoners, although Brown's administration has said the backlog of unheard cases is not its responsibility.
The state's prisons have long been beset by problems in the delivery of medical care and psychiatric services, inmate suicides and lawsuits over other conditions. The three judges ruled that the problems were due to overcrowding and in 2009 ordered the state to remove about 43,000 inmates.
The state moved some prisoners to private facilities, built a new medical prison and kept more than 20,000 prisoners and parole violators in county jails rather than send them to state prisons. Officials have also signed agreements with private prison operators for almost 3,800 beds at three facilities.
The latest of those is an $86-million, three-year contract announced Tuesday to take over a California City prison that houses federal immigration detainees.
But a corrections department spokeswoman said Tuesday that the state still has 4,400 more prisoners than the cap permits.
As part of its contract, Corrections Corp. of America will make the first $10 million in upgrades that might be needed to house California's higher-security inmates. After that, the bill falls to California taxpayers.
If Brown doesn't want to give up yet on his effort to be free of the inmate cap, one expert said, he might still be able to find ways to contest the cap before a lower court.
There is no "federal order that is not appealable," said Kent Scheidegger, an official of the Criminal Justice Legal Foundation. "It is a matter of finding" the right procedure, he said.
Scheidegger's Sacramento-based group submitted a brief to the Supreme Court on behalf of four former California governors, siding with Brown by arguing that the cap is unreasonable in light of the improvements California has made.
In the meantime, prisoners' lawyers are pressing for even greater court intervention, seeking new orders on treatment of inmates.
"Prisoners are still suffering from terrible healthcare," said Don Specter of the Prison Law Office, which represents inmates in the federal court cases.
"Reports from the court experts still show that prisoners are at great risk of injury or death from the lack of adequate medical care," he said.
