WASHINGTON (Reuters) - The Supreme Court rebuffed the state of Alabama on Monday by deciding not to intervene in a case where federal judges blocked a state law that criminalizes the harboring of illegal immigrants. By refusing to hear Alabama's appeal of the Obama administration's lower court victories, the justices steered clear of a hot-button debate at a time when Congress is engaged in writing legislation to overhaul immigration laws. Both a federal judge and an appeals court agreed with the White House that federal law trumped a provision in Alabama state law that made it illegal to harbor or transport anyone in the state who had entered the country illegally. The appeals court ruling remains intact as a result of the Supreme Court's refusal to intervene. A brief order issued by the Supreme Court on Monday said Justice Antonin Scalia disagreed with the decision not to hear the case. The case before the court concerned only the harboring provision. Other parts of the Alabama law are being challenged also by the Obama administration and private groups. Enacted in 2011, the Alabama law is considered one of the toughest state immigration statutes in the country. The law also made it illegal to encourage people to either enter or stay in the state in violation of federal immigration laws. In two separate decisions, the Atlanta-based 11th U.S. Circuit Court of Appeals upheld injunctions against the harboring provision and other parts of the law in August 2012. Although the high court declined to hear the case, the same issue could resurface in the high court because nine other states have similar laws that have been challenged. Often the court will wait until several different lower courts have ruled on a legal issue before providing the final word. "Hopefully, Justice Scalia's vote indicates that once those additional courts have weighed in, the Supreme Court will be willing to grant review," said Joy Patterson, a spokeswoman for Alabama Attorney General Luther Strange. The Alabama case will now return to the district court, where the judge will, among other things, consider the impact of a Supreme Court ruling last year in which the justices partially upheld Arizona's similar immigration law, Patterson added. A separate challenge to the Alabama law brought by private groups, including the American Civil Liberties Union, will also proceed in the district court. Cecillia Wang, an ACLU attorney, said the aim will be to prove that parts of the law that were not already blocked "are in fact causing constitutional violations." Editing by Howard Goller and Mohammad Zargham