ABC News' Kristina Zverjako and John Parkinson report:

Update:

The House is likely to pass a Senate-approved version of the Violence Against Women Reauthorization Act Thursday, sending the bill to President Obama for his signature.

A rule approved in the House Rules Committee tonight allows an up-or-down vote first on a controversial House GOP version of the measure as a substitute amendment. If that passes, then the GOP version becomes the underlying bill. If it fails, the House would be left with an up-or-down vote on the Senate-passed bill. With insufficient support for the GOP bill, the vote on the Senate bill appeared almost certain to pass with bipartisan support.

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House Democrats earlier said they were not satisfied with the Republican-crafted version of the Violence Against Women Reauthorization Act, pledging to oppose it if it came up for a vote later this week in the House.

Speaking at the Capitol today, House Minority Leader Nancy Pelosi, D-Calif., called the Republican measure a step down from the Senate bill that passed with bipartisan support earlier this month, saying that "this bill is weaker than the Senate bill, weaker than the current law."

House Democrats said that the Republican-proposed version up for consideration this week does not provide adequate protection for the sexual crime victims associated with human trafficking or members of the lesbian, gay, bisexual, transgender and Native American communities.

Rep. Gwen Moore, D-Wis., who has previously detailed her experience as a sexual assault victim on the House floor, asked her GOP colleagues Tuesday afternoon to "stand up for what is right and righteous, and reconsider this ill-conceived legislation, and work together with us to pass the bipartisan Senate bill."

A House GOP leadership aide defended the latest Republican proposal, contending that House Democrats are using the politically contentious issue as a way to divide the Republican Party. Some members of the Republican conference have pressured leadership to allow a vote on the Senate bill rather than delay passage with another political fight.

The House GOP aide said the Republican leadership believes its bill makes significant improvements to the Senate bill, claiming that every woman is protected from discrimination.

The House could vote to reauthorize the Violence Against Women Act as soon as Thursday.