The Obama administration had challenged the state law, saying it usurped the role of the federal government. A federal judge agreed in part and issued an injunction against key parts of the law. A federal appeals court panel then decided the judge had the authority to issue the injunction.
Arizona argues that the federal law fails to control illegal immigration.
"Arizona enacted the Support Our Law Enforcement and Safe Neighborhoods Act to address the illegal immigration crisis in the state," the state's petition to the high court said.
"The four provisions of [the state law] enjoined by the courts below authorize and direct state law enforcement officers to cooperate and communicate with federal officials regarding the enforcement of federal immigration law and impose penalties under state law for non-compliance with federal immigration requirements.
"The question presented is whether the federal immigration laws preclude Arizona's efforts at cooperative law enforcement and impliedly pre-empt these four provisions ... on their face," the petition said.
The injunction bars enforcement of provisions of the law requiring police officers to question people about their immigration status during routine law enforcement operations, if officers have reason to suspect people are not in the United States legally.
The injunction also blocks a provision that criminalizes failure to apply for or carry alien registration papers, and a third that makes it illegal "for an unauthorized alien to solicit, apply for or perform work." Another blocked provision allowed police to arrest aliens thought to have committed a deportable offense.
Following her injunction last July, U.S. District Judge Susan Bolton received hundreds of threats, the U.S. Marshals Service said.
Bolton acknowledged the state law was enacted against "a backdrop of rampant illegal immigration, escalating drug and human trafficking crimes and serious public safety concerns."
The U.S. Supreme Court should hear the case later this term, and hand down a decision before recessing for the summer in late June. Justice Elena Kagan, who helped form the federal challenge to the state law as U.S. solicitor general, will not participate in the case.