WASHINGTON — After a fierce fight, full of gender politics, the House passed a Republican bill on Wednesday to combat violence against women, over objections from President Obama and other Democrats, who said it would reduce protections for many battered women, including lesbians, American Indians and illegal immigrants.

The 222-to-205 vote clears the way for negotiations with the Senate, which passed a more expansive version last month by a vote of 68 to 31.

Some version of the legislation is likely to become law before elections this fall. But first, Democrats said, they want to force the likely Republican presidential nominee, Mitt Romney, to choose between the House bill and the Senate measure, which was approved with support from 15 Republicans.

Mr. Obama threatened to veto the House bill. But it passed, with support from 216 Republicans and 6 Democrats. Twenty-three Republicans joined 182 Democrats in voting against the bill.