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Two House Republicans, Reps. Darrell Issa of California and Tom Cole of Oklahoma, last year offered a compromise that would allow non-Indian defendants to request that their cases be moved to federal courts, but the session ended before a deal could be reached. Mr.  Cole is one of two House members claiming Indian heritage.

The Violence Against Women Act provides grants to state and local offices for legal assistance, transitional housing, law enforcement training, stalker databases and domestic violence hotlines. It also established the Office on Violence Against Women within the Justice Department.

The programs authorized under the act are still in place. But without reauthorization of the law, they cannot be expanded or improved. The Senate bill would consolidate 13 existing programs into four and set aside some $659 million over five years for the programs, down 17 percent from the last reauthorization in 2005. The bill also would give more emphasis to sexual assault prevention and take steps to reduce the rape kit backlog. In a concession to Republicans, it removes a provision in last year’s bill that would have increased visas for immigrant victims of domestic violence.