The Senate appears likely to approve a measure Thursday to reauthorize the 18-year-old Violence Against Women Act, after Republicans decided to largely postpone a battle over some provisions of the sprawling provision dealing with hot-button issues of immigration and new protections for gay men and lesbians.

Republicans have shifted their attention to the House, where a group of Republican women announced Wednesday that they will introduce an alternative version of the legislation.

The strategic shift came against the backdrop of a heated campaign trail battle for the votes of women. Democrats had been hammering Republicans for the objections, citing it as the latest example of GOP hostility to issues important to women.

Republicans countered that Democrats had inserted politically charged issues into what had been a bipartisan domestic violence program, and presumptive Republican presidential nominee Mitt Romney announced he supported reauthorizing the law.

The differences between the competing bills will have to be worked out in coming months. Those negotiations will probably feature a battle of finger-pointing, in which both parties seek political advantage while accusing the other of politicizing the sensitive issue of domestic and sexual violence.

Senate Democrats note their legislation was written in consultation with victims advocates and was introduced with the support of a filibuster-proof 61 senators, including eight Republicans.

“It is a shame that we have gotten to this point, to have to stand here to work to pass legislation that has consistently received broad bipartisan support,” Sen. Patty Murray (D-Wash.) said.

The legislation reauthorizes a series of grants that provide funding to local law enforcement to combat domestic and sexual violence, as well as shelters and advocacy programs that assist victims.

Originally introduced in 1994, the Violence Against Women Act was reauthorized with little controversy in 2000 and 2005 and has been credited with raising awareness about the problems of domestic abuse.

The new legislation would consolidate some programs. It would also slash funding authorized for the measure by nearly 20 percent — to $659.3 million — a cut agreed to by members of both parties that has distressed victims’ advocates.

Three provisions have proven controversial with some Republicans. One would add new language barring discrimination in programs funded through the act on the grounds of sexual orientation or gender identity.

Another would allow law enforcement to issue as many as 5,000 more visas annually to illegal immigrants who cooperate in prosecutions of major crimes. That would expand a program initiated in 2000 that allows up to 10,000 visas each year to encourage immigrants to report crime without fear of deportation.

Another section of the law would give federal courts new authority over non-Native American men who abuse Native American women on tribal reservations, a proposal some Republicans believe is constitutionally problematic.

The Senate authors of the bill said the items dealing with Native Americans, lesbians and gays merely specify that services intended to be available to all cannot be excluded from the law’s reach.

Rep. Sandy Adams (R-Fla.), leading the House effort, said the Republican measure will not address those topics.

“We are not going to be looking at the controversial issues that will detract from what is actually VAWA,” she said. “We need to make sure that we don’t allow this bill to become a political issue. This is a bipartisan bill, and it should stay as such.”

The Senate will probably vote Thursday on a Republican alternative authored by Sen. Kay Bailey Hutchison (R-Tex.) that would also avoid the controversial topics. She said her bill strengthens the measure in other ways, such as by requiring a higher percentage of grant money to be spent directly on abuse victims.

But, she said that if her version of the legislation does not pass, she will support the Democratic version and predicted both chambers will arrive at a compromise by the November election.

“There are things that are imperative that we do,” she said. The bill “is good, except for a few things.”

Democrats said they believe the effort to offer alternatives to a measure with more than 60 co-sponsors is a sign that Republicans are not as supportive of the reauthorization effort as they claim.

“The fact that there are significant-enough changes to introduce a whole new bill raises questions about what the real effort is here,” said Sen. Jeanne Shaheen (D-N.H.).

The debate over the issue comes as Congress is increasingly consumed by legislative initiatives inspired by the political skirmishes of the presidential campaign trail.

On Friday, the House will consider Republican-authored legislation to prevent student loan rates from rising from 3.4 to 6.8 percent on July 1, and the Senate will take up the issue next month, an issue that President Obama has been hammering for his reelection effort.

Congressional Republicans were boxed in on the student loan issue after Romney announced he supported extending lower loan rates.

Republicans have been working to similarly isolate Obama from congressional Democrats on the issue of the construction of the Keystone XL pipeline. The administration has said further environmental reviews are necessary before approving a stretch of the oil pipeline in Nebraska.

But an increasing number of Hill Democrats are supporting a Republican push to let Congress require approval of the project.