The Obama administration's notice to U.S. public schools on Friday that transgender students must be allowed to use the bathroom of their choice raised questions about federal funding and legal authority that could play out for months.

Some Republicans and religious conservatives pushed back against the administration's non-binding guidance to schools, escalating tensions over the volatile issue of lesbian, gay, bisexual and transgender Americans' civil rights.

Texas Attorney General Ken Paxton said in a statement that the guidance "must be challenged." A Tea Party champion, he said in a statement: "If President Obama thinks he can bully Texas schools into allowing men to have open access to girls in bathrooms, he better prepare for yet another legal fight."

The U.S. Education and Justice departments, in a letter, told school districts nationwide that, while the new guidance carries no legal weight, they must not discriminate against students, including based on their gender identity.

The guidance contained an implicit threat that school districts defying the Obama administration's interpretation of the law could face lawsuits or be deprived of federal aid.

"Our guidance sends a clear message to transgender students across the country: here in America, you are safe, you are protected and you belong, just as you are," Vanita Gupta, head of the Justice Department's Civil Rights Division, said in a statement with the letter sent to school districts nationwide.

The guidance came at a time when the Justice Department and North Carolina are battling in federal court over a state law approved in March prohibiting people from using public restrooms not corresponding to their gender assigned at birth, while other states weigh similar measures.

North Carolina's law was the first to ban people from restrooms in public buildings and schools not matching the sex on their birth certificate. Mississippi has enacted legislation similarly viewed as discriminatory by civil and gay rights groups, and Tennessee and Missouri considered similar measures.

The letter to the schools from Washington said that, to get federal funding under existing rules, a school has to agree not to treat students or activities differently on the basis of sex. That includes not treating a transgender student differently from other students of the same gender identity, officials said.

The American Civil Liberties Union said the guidance would help make students "free to bring their whole selves to school."

In a sign of what defiant states may face, the Justice Department this week asked a U.S. district court in North Carolina to declare the state in violation of the 1964 Civil Rights Act and order it to stop enforcing the ban.

Americans are divided over which public restrooms should be used by transgender people, according to a Reuters/Ipsos poll, with 44 percent saying people should use them according to their biological sex and 39 percent saying they should be used according to the gender with which they identify.

Republican Texas Lieutenant Governor Dan Patrick said on Friday that he would not abide by Obama's guidance and that the state would find a way to fill any funding gap.

An Arizona-based conservative Christian activist group, the Alliance Defending Freedom, said the U.S. guidance lacks legal authority. The group said it has already filed two lawsuits, one in Illinois and one in North Carolina, over related issues.

Donald Trump, the presumptive Republican presidential nominee, was less critical in several television interviews.

"Everybody has to be protected ... but it's a tiny, tiny portion of the population," Trump told Fox News, adding that the issue is one that should be left up to individual states.