The veto threat sets up another showdown between Obama and his congressional allies and Republicans, on an issue — protections for women — that Democrats are trying to highlight for the November election.

Specifically, the administration said it rejects the GOP bill because it fails to give tribal authorities jurisdiction over non-Indians in domestic violence cases, like the Senate bill does.

The administration also said the bill does not include language prohibiting discrimination against LGBT victims in VAWA grant programs, and "eliminates the path to citizenship for U visa holders," which illegal immigrants can use to stay in the United States if they are victims of domestic abuse or rape.

"These proposals senselessly remove existing legal protections, undermine VAWA's core purpose of protecting victims of sexual assault and domestic violence, frustrate important law enforcement objectives, and jeopardize victims by placing them directly in harm's way," the statement said.

House Republicans have said their bill is similar to the bill passed by the Senate, S. 1925, although it does not expand access to U visas like the Senate bill does. Republicans have said this expansion would increase the deficit.