ALBANY, N.Y. (Reuters) - Dozens of large U.S. companies on Friday backed the Obama administration's bid to strike down a North Carolina law restricting the use of public bathrooms by transgender people, saying the law hurts their recruitment efforts and could discourage investment in the state.

In a friend-of-the-court brief filed in federal court in Winston-Salem, North Carolina, 68 companies including Apple Inc , Bloomberg LP, Microsoft Corp, General Electric Co and Nike Inc, said the law, known as H.B. 2, should be blocked pending the outcome of the U.S. Department of Justice's lawsuit seeking to have it overturned.

"H.B. 2 and the naked, invidious discrimination it condones is already damaging (some companies') ability to recruit and retain a diverse workforce and is imposing a substantial disincentive to investment and commerce in the state, directly impacting their bottom line," the brief says.

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North Carolina Governor Pat McCrory, a Republican, said in a statement on Friday that businesses were free to adopt their own anti-discrimination policies, and that the law was designed to protect the privacy of the state's residents in public places.

"It's disappointing that some companies are joining the Obama Administration's position which jeopardizes those long-held expectations of privacy," he said.

The state law, which was passed in March, requires people to use public bathrooms that correspond with the sex on their birth certificates even if it conflicts with the gender they identify with. The Justice Department says that violates federal civil rights laws prohibiting gender discrimination in employment and education.

The lawsuit is just one front in a nationwide debate over civil rights for transgender people. Since 2012, several federal agencies have separately said that existing laws include protections for transgender people in employment, education and public accommodations, but federal courts have not settled the issue.

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Separately on Friday, 10 states including Michigan, Ohio and Kansas filed a lawsuit in federal court in Nebraska challenging a May 13 letter the Justice Department sent to states warning them that restricting public bathroom use by transgender people was a violation of federal law that could lead to cuts in federal education funding.

Thirteen states are mounting a similar challenge to the administration in a lawsuit in federal court in Texas.