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AUSTIN (AP/CBSDFW) – Texas Gov. Greg Abbott is giving his first clear support for a “bathroom bill” that supporters say is similar to North Carolina’s recent compromise but opponents still reject as discriminatory.

Abbott on Tuesday said he’ll work on a bill with the Republican-controlled Legislature before it adjourns in May. His significant endorsement follows months of relative silence over a state Senate measure that would require people to use public bathrooms that correspond with the sex on their birth certificate.

But Abbott is now backing a House version that sets aside that language. It instead bans cities from adopting nondiscrimination ordinances that would apply to restrooms.

“I applaud the House and Senate for tackling an issue that is of growing concern to parents and communities across Texas who are now looking to the Legislature for solutions,” Abbott said in a statement. “Rep. Simmons is offering a thoughtful proposal to make sure our children maintain privacy in our school bathrooms and locker rooms.  As the debate on this issue continues, I will work with the House and Senate to ensure we find a solution and ultimately get a bill to my desk that I will sign into law.”

“Besides costing $3 billion in loss, HB2899 discriminates against transgender Texans,” said Glaad president and CEO Sarah Kate Ellis in a tweet Tuesday.

The NCAA is again letting North Carolina host championship events under that state’s newly revised bathroom bill. On Tuesday, the NCAA awarded Texas several future championship sites.

(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)