Gov. Arnold Schwarzenegger signed a letter Monday asking President Bush to include $950 million in next year's federal budget to help offset the cost of jailing illegal immigrant criminals in state prisons.

Under a federal program, called the State Criminal Alien Assistance Program, states receive money to reimburse them for the cost of housing illegal immigrant inmates. But the president has proposed eliminating the program in recent years.

"Until the federal government can achieve its goal of restoring safety and security throughout our border regions, every effort should be made to compensate the state and local governments who have stepped up to fill this gap by policing and incarcerating criminal aliens at their own considerable expense," according to the letter.

Since 1990, when the payments were first written into federal law, reimbursements have shrunk. Last year, Bush proposed no funding for the program, but Congress restored $405 million, about 40 percent of which went to California. State officials say illegal immigrants cost the California prison system $750 million a year.

Governors from 10 other states also signed the letter, including those from Washington, New Jersey, Arizona and New Mexico.