WASHINGTON (CNN) -- The Supreme Court has refused to review Alabama's controversial immigration crackdown law, and whether a provision over harboring illegal immigrants conflicts with broad federal authority.

The justices issued a brief order Monday, which means the law for now will not be allowed to go into effect.

The specific section under consideration by the high court would make it a crime to assist those entering the U.S. without authorization -- by transporting, inducing, or encouraging them to stay in Alabama.

HB56, passed by the legislature this summer in 2011, would also have given state and local officials the power to check the immigration status of public school students and to detain suspected undocumented immigrants without bond.

Those provisions are being challenged separately in lower courts.

The Alabama law had not been enforced, pending the outcome of court appeals. Nine states had sided with Alabama and had asked the high court to intervene in the current dispute, but the justices gave no reason for their refusal.

The U.S. Justice Department argued it alone has the power to enforce any immigration violations, pre-empting any separate state action.

The case is Alabama v. U.S. (12-884).

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