AUSTIN, Texas — A federal judge declared a same-sex marriage ban in deeply conservative Texas unconstitutional on Wednesday, but will allow the nation’s second-most populous state to enforce the law pending an appeal that will likely go to the U.S. Supreme Court.

Judge Orlando Garcia issued the preliminary injunction after two gay couples challenged a state constitutional amendment and a long-standing law.

Garcia said the couples are likely to win their case and the ban should be lifted, but said he would not enforce his ruling pending one by the 10th Circuit Court of Appeals, which already is hearing two other states’ cases. He also will give Texas time to appeal to the 5th Circuit Court of Appeals in New Orleans.

Texas Attorney General Greg Abbott, who also is the leading Republican candidate to succeed Gov. Rick Perry, promised to appeal the decision to the New Orleans court.