WASHINGTON — House Republican leaders bowed to pressure from within their own party and cleared a path for House passage on Thursday of the Senate’s bipartisan reauthorization of the Violence Against Women Act.

The House Rules Committee on Tuesday night approved a bifurcated process to consider the legislation, which would broaden the landmark 1994 law. The House will vote on a Republican version on Thursday, which contains provisions that weaken a Senate version that empowers Native American courts to prosecute non-Indians accused of violence on tribal land. The House version also does not extend the reach of domestic violence programs to those in same-sex relationships.

If that version fails to win passage, the House will take up the Senate-passed version — at this point the most likely outcome. That would ensure a swift White House signing ceremony.

The Senate passed that version this month, 78 to 22, with 23 Republicans voting yes, up from 15 last year.