A House Republican has withdrawn, for now, an amendment to repeal President Obama’s lifting of a ban on transgender troops but warned Defense Secretary James Mattis that he must act to restore the longtime exclusion or face a legislative revolt.

The amendment did provide conservatives on the House Armed Services Committee on Wednesday night a forum to condemn the former president’s decision on grounds that it would drive up medical costs, reduce combat readiness and subject troops to embarrassing encounters.

Mr. Mattis faces a Saturday deadline, inherited from former Defense Secretary Ashton Carter, to approve the recruitment of transgender people. Mr. Carter last summer ordered that transgender troops on duty no longer face discharge. He assigned commanders the task of shepherding gender reassignment procedures.

Rep. Vicky Hartzler, Missouri Republican, offered the repeal amendment, which also would provide honorable discharges to all currently serving transgender service members.

She delivered a five-minute speech and then announced that she would withdraw the language to the fiscal 2018 defense budget, giving time for Mr. Mattis to revoke Mr. Carter’s order.

Mr. Mattis has said he does not plan any reversals unless the military shows him the policies have created problems.

“This policy is ill-conceived and contrary to our goals of increasing troop readiness,” Mrs. Hartzler said.

She asked why the military bans recruits for such relatively minor defects as flat feet but now is going to induct people with gender dysphoria. They will require a “lifetime of hormonal treatment, psychiatric treatment and surgeries [that] could cost taxpayers $1.5 billion over 10 years,” she said.

“It also is a threat to our readiness,” Mrs. Hartzler said, adding that people undergoing sex reassignment cannot deploy and need more than 200 days off.

“Why would we purposely recruit individuals to serve who we know cannot serve?” she said.

Rep. Steve Russell, Oklahoma Republican, read from Army training slides, including some that tell soldiers how to deal with a pregnant man or the sight of male genitalia in the women’s showers.

“‘His pregnancy,’” Mr. Russell said, reading from the slide.

“Transgender soldiers under these vignettes are not required or expected to modify or adjust their behavior, but everyone else is, violating their privacy, their rights, their morality and their unit cohesion,” he said. “I suggest, Mr. Chairman, that we have lost our way as a nation.”

Rep. Niki Tsongas, Massachusetts Democrat, said Mr. Carter ordered extensive studies by the Rand Corp. think tank and other researchers, who concluded that allowing 2,400 transgender troops to stay on active duty would not hurt readiness. She said the service chiefs signed off on the policy.

“I urge my colleagues to refrain from relying on unfounded figures and assumptions to change a policy that was designed to open service to all who can meaningfully contribute to the military and their country,” Ms. Tsongas said.

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