WASHINGTON — Senate Republicans made temporary peace with Democrats to approve the reauthorization of a popular law designed to help prevent and respond to domestic and sexual abuse.

Passage of the Violence Against Women Act on a 68-31 vote gives momentum to the legislation. But the bill still faces hurdles in the House.

Usually the reauthorization has bipartisan support. But this year it has become enmeshed in the partisan wrangling that has dominated this Congress.

The legislation now goes to the House, where Republican women are introducing their own proposal.

The Violence Against Women Act, originally written by Vice President Joe Biden when he was a senator, was first approved in 1994. The current authorization expired last year, but the programs have already been funded through the end of the fiscal year, Sept. 30. This bill, if signed into law, would reauthorize the programs for the next fiscal year.

Approval has been a priority, given President Barack Obama’s desire to solidify his standing among women voters. Republicans have claimed that Democrats were using the act for political gain during an election year.