WASHINGTON — The Senate took up the Violence Against Women Act Monday, seeking to remedy Congress’ failure last year to extend and expand a law protecting women from domestic abuse while broadening its coverage to include Native Americans, gays and lesbians.

Both the Democratic-led Senate and the GOP House attempted last year to upgrade the 1994 law which expired in 2011. But leaders of the two chambers were unable to span the partisan divide and reach a compromise. With Republican losses among women voters in the November election still a fresh memory, Senate advocates are hoping that it will be easier to find common ground with House Republicans.

The Senate bill, while making minor concessions to meet GOP concerns, is essentially the same as the measure that passed that chamber last April on a 68-31 vote. It focuses on ensuring that college students, immigrants, Native Americans and gays, lesbians, bisexuals and transgender people have access to anti-abuse programs. In contrast to the House version of the update of the legislation, the Senate bill has bipartisan backing and is expected to have little difficulty in garnering the necessary 60 votes to be moved to the floor. A final vote could come by the end of the week.

The Violence Against Women Act, or VAWA, “has been extraordinarily effective” in combating domestic violence, Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., said in a letter urging the support of his colleagues. He said that since VAWA was first passed the annual incidence of domestic violence has fallen by more than 50 percent.

During election campaigns last year Democrats seized on the congressional stalemate over VAWA in claiming that Republicans did not represent the best interests of women.

Sen. Patty Murray, D-Wash., a key sponsor, said she was encouraging moderate Republicans in the House to sign onto the Senate bill. House Democrats have introduced a bill that is identical to the Senate measure.

House Republicans also support the act, but last year they objected to language in the Senate bill on gays and lesbians.

“We continue to work with VAWA advocates on the best path forward to ensure we protect women and prosecute offenders,” said Doug Heye, a spokesman for House Majority Leader Eric Cantor, R-Va.

Last year Cantor unsuccessfully tried to work out a deal with Vice President Joe Biden, who as a senator was instrumental in passing the 1994 act. This year the top woman in the House GOP leadership, Rep. Cathy McMorris Rodgers of Washington, is expected to spearhead the Republican effort.

House Republicans also opposed a Senate provision that would have given limited powers to tribal authorities to prosecute non-Indians accused of assaulting their Indian partners on tribal lands. Currently, non-Indians who batter their spouses often go unpunished because federal authorities don’t have the resources to pursue misdemeanors committed on reservations.

The National Congress of American Indians says violence against Native American women has reached “epidemic proportions,” citing findings that 39 percent of American Indian and Alaska native women will be subjected to violence by a partner in their lifetimes. It cited a 2010 government report finding that U.S. attorneys declined to prosecute half of violent crimes occurring in Indian country, and two-thirds of the declined cases involved sexual abuse.

The GOP’s desire to improve its standing among women voters has given Republicans another incentive to find common ground on VAWA, and Debby Tucker, executive director of the Austin-based National Center on Domestic and Sexual Violence, said she was “cautiously optimistic” that politicians could put aside their differences. “I just hope that they realize that people’s basic health and safety have to be elevated above political considerations,” she said.

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 would also 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.