The 11th U.S. Circuit Court of Appeals last year issued an injunction against a section of the state law that had made it a crime to harbor an illegal immigrant, al.com reported.
No opinion was issued in declining Alabama's request for the court to hear oral arguments in the case.
Justice Antonin Scalia disagreed.
In appealing the 11th Circuit's decision, the state argued the court had erred in ruling the Alabama law was pre-empted by the federal government's laws on harboring.
The Alabama law had been criticized by immigrant rights groups as excessively harsh.
Alabama had argued the provisions did not interfere with federal immigration law and that business owners could legally sue companies who flout immigration law.
Several provisions of the Alabama laws have been blocked, including a requirement that schools gather immigration data about new students and another that made it a crime for a person who illegally entered the United States to ask for work.
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