Ending a 16-month battle with the Senate, the House of Representatives voted 286-138 to approve the plan as part of an expansion of the 1994 Violence Against Women Act. Republican opponents relented after failing to win enough votes to reauthorize the law without the provision.
The bill now goes to President Barack Obama, who said he'd sign it.
"I'm ecstatic," said Deborah Parker, the 42-year-old vice chairwoman of the Tulalip Tribes, who came to the Capitol last year to recount how she had been sexually and physical abused while growing up on the reservation.
Parker and other tribal officials lobbied hard for a new law in response to a 1978 Supreme Court ruling that tribes had no authority to try or punish non-Indians. The case involved a Washington state man whom the Suquamish Indian Tribe ordered to appear in tribal court after he was cited on charges of resisting arrest and assaulting a police officer.
"This is a long-delayed and hard-won victory for millions of women in this country," said Sen. Patty Murray, D-Wash., who made the issue a top priority after Congress allowed the law to expire in 2011.
The law, once signed, will allow tribes to try non-Indians only for rape and other crimes involving domestic abuse. While many opponents say the reauthorized law would be unconstitutional, backers say a narrow expansion probably would survive a court challenge.
Backers of the new law say it's needed because too many local authorities don't want to investigate crimes committed on reservations. And they say the situation has become severe: Indian women are murdered at more than 10 times the national average, and more than one in three will be raped in their lifetimes, according to the National Task Force to End Sexual and Domestic Violence Against Women. That rape rate is twice as high as it is for other ethnicities.
The bill also would expand federal investigative assistance to include gay, lesbian, bisexual and transgender victims and would allow more illegal immigrants who are victimized to get temporary visas to stay in the United States.
Murray estimated that at least 30 million more women will be eligible for help.
In a statement, Obama credited the Violence Against Women Act with saving "countless lives" and changing the way the nation has responded to domestic abuse.
"Renewing this bill is an important step towards making sure no one in America is forced to live in fear, and I look forward to signing it into law as soon as it hits my desk," the president said.
Republican Rep. Doc Hastings of Washington state said "there is no doubt" that the law would be struck down, and he accused Democrats of hijacking the law to advance other political agendas. He said he'd always voted to reauthorize the law before but that it had gotten caught up in a "political stampede" this time around.
"In a tribal court, constitutional protections and the Bill of Rights do not apply," Hastings said. "Under the bill, a non-Indian citizen tried in a tribal court has no right to appeal to a federal court, lacks the guarantee of due process, has no right to an impartial jury of one's peers and more. A vote in favor of the bill was a vote to deny U.S. citizens their Bill of Rights."
Congress spent much of the last session at loggerheads over the issue, with Murray and other Democrats accusing Republicans of dragging their feet in protecting women.
After the Senate voted 78-22 two weeks ago to reauthorize the bill as one of its first acts in the new Congress, it became clear that Republicans wanted to avoid a replay of the fight.
The House voted on two bills: In the first, 60 Republicans joined Democrats to defeat an amendment that would have reauthorized the law without adding the extra protections for Indian women, immigrants and gay, lesbian, bisexual and transgender victims. In the second, 87 Republicans backed the broader Senate bill.
Murray credited moderate House Republicans as helping to turn the tide by demanding a vote on the Senate plan.
Republican Rep. Shelley Moore Capito of West Virginia said she had backed the Senate plan as a way to help more children escape domestic violence. She told the story of a little boy who died when he was struck and killed after jumping out of a car on a freeway when his mother's boyfriend began beating her.
Freshman Republican Rep. Kevin Cramer of North Dakota told the story of his 5-year-old son, whom he and his wife adopted three years ago: The boy had watched his stepfather beat his mother for half an hour, killing her.
"I know the scourge of violence against women personally," Cramer said.
Democratic Rep. Rick Larsen recalled a case in 2000 in his district in northwestern Washington in which an immigrant woman named Anastasia King was murdered by her husband.
"Domestic violence does not discriminate. With this bill, domestic violence protection will no longer discriminate," Larsen said.
Backers of the law said they wouldn't have prevailed if they hadn't been able to put a human face on domestic abuse. Murray, in particular, had urged victims to go public.
After the vote, Murray said Parker's story - she appeared with Murray and other Democratic senators at a Capitol Hill news conference - had played a key role in getting the law reauthorized.
Parker said her abuse began when she was a toddler and happened repeatedly until the summer after third grade. But she said it was never reported to police because they wouldn't have bothered to investigate anyway.
"I think Deborah Parker made the absolute difference at the absolute critical time, being here, standing up and making her personal story become the face of what this was about," Murray said. "It was an act of courage and it changed the whole debate."
More Nation & World Headlines
World leaders gather to try to save Earth from overheating Pope urges peace while visiting C. African Republic mosque 5:25 p.m. Rubio: Radical jihadists using refugee crisis as cover McCarthy predicts no gov’t shutdown over Planned Parenthood Feds say U of Chicago threat a response to police shooting Bond set at $1.5M for Chicago officer who fatally shot teen House may move quickly to overhaul visa waiver program Candy, the other Carson with gifted hands
Our new comment system is not supported in IE 7. Please upgrade your browser here.