Both bills set policy for the Defense Department for 2013, and both authorize the spending of about $630 billion, although the House bill authorizes about $3 billion more — a difference that will have to be worked out in conference.

Several other pieces of the bills will also have to be reconciled, including language in the Senate bill that would require DOD to start eliminating tens of thousands of civilian workers over the next five years. Elsewhere, the Senate bill has a permanent ban on moving detainees from Guantánamo Bay to the United States, language that is not in the House bill.

The House bill ends a program allowing DOD to use biofuels and bans same-sex ceremonies in military facilities, and also creates a costly East Coast defense program — all provisions that are not in the Senate bill.

After approving a motion to conference with the Senate by unanimous consent, the House voted in favor of a Democratic motion to instruct conferees. The motion instructs House negotiators to support language in the Senate bill that requires DOD to set out a plan for promoting the security of women and girls in Afghanistan as the U.S. transitions out of that country.

"Just this week, we had reminder of those security concerns," Rep. Susan Davis (D-Calif.) said on the House floor. "On Monday, the director for women's affairs was killed in the Laghman province. She replaced the previous director who was also assassinated just six months ago.

"It is heartbreaking to hear of these female leaders being assassinated in an area that is trying so hard to move their people and their country forward."

Republicans overwhelmingly agreed to the motion, which passed in a 399-4 vote. The four "no" votes came from Republicans: Reps. Justin AmashJustin AmashThe 13 House Republicans who voted against the GOP tax plan House Judiciary advances warrantless wiretapping reform bill The Hill's Whip List: Where Republicans stand on tax-reform bill MORE (R-Mich.), Walter Jones (R-N.C.), Thomas Massie (R-Ky.), and Ron Paul (R-Texas).

"We need to do everything we can do to ensure the safety of women," House Armed Services Committee Chairman Buck McKeon (R-Calif.) said.

"When you withdraw the troops, it's a serious time, it's a dangerous time. As we pass the effort over to the Afghan security forces to provide the protections and keep the gains that we've made, it's very important that they don't fall back into the same way that they've treated women in the past."

The House also voted 351-53 to keep portions of the House-Senate conference closed, due to the classified materials that will be discussed in those meetings.