WASHINGTON, May 17 (Reuters) - The House of Representatives stripped a requirement that women register for the military draft from a sweeping annual defense policy bill on Tuesday, but supporters of the provision said they would keep pushing for its passage.

Democrats accused the committee's Republican leaders of using an underhanded ploy to undercut the House Armed Services Committee, which had approved the amendment, and avoid what could be a difficult vote for some party members.

"They don't want to subject their members to a vote on equality for women," Representative Steny Hoyer, the No. 2 House Democrat, told reporters.

Republican Representative Mac Thornberry, chairman of the House Armed Services Committee, said the amendment was removed because it violated House budget rules due to the cost of registering women. He said it was replaced with an amendment calling for a broad review of the Selective Service.

The House Rules Committee set up removal of the amendment from the National Defense Authorization Act, or NDAA, during a meeting late on Monday. It was taken out of the bill via a procedural vote on Tuesday afternoon.

But the effort is not dead. The Senate Armed Services Committee included a similar amendment in its version of the NDAA, and it has bipartisan support in the Senate.

The Senate's Republican Majority Leader, Mitch McConnell, said he believed women should register, although he did not expect the country to reinstate the draft.

"Given where we are today with women in the military performing virtually all kinds of functions, I personally think it would be appropriate for them to register just like men do," McConnell told a news conference.

Defense Secretary Ash Carter announced last year that all combat positions would be open to women, which immediately prompted calls that women also should be required to register. That worried some social conservatives uncomfortable with the blurring of men's and women's traditional roles in society.

The U.S. military has been an all-volunteer force since the 1970s, but young men have been required to sign up for the Selective Service in case the draft is reactivated.

To become law as part of the NDAA, a version of the defense bill with the amendment would have to be approved by the full House and Senate, and signed by President Barack Obama.

(Additional reporting by Richard Cowan; Editing by Dan Grebler)