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Critics have said the law, known as SB 1070, will lead to racial profiling of Hispanics in Arizona. But the Obama administration has not challenged the law on those grounds, instead focusing on issues of federal versus state power.

Mr. Verrilli said Arizona’s goal is to try to force the federal government to change its priorities, but he said those policies are designed at the national level in order to balance concerns over available resources and international relations.

“What [Arizona is] going to do is engage effectively in mass incarceration,” he said. “It poses a very serious risk of raising serious foreign relations problems.”

Some of the justices, including Justice Samuel A. Alito Jr., seemed concerned that allowing police to perform immigration checks could end up leading citizens being held even longer during stops by police.

Mr. Clement said the law still complies with the Fourth Amendment’s limits on unreasonable searches.

Anticipating an unfavorable ruling, Sen. Charles E. Schumer, a New York Democrat who is a critic of the Arizona law, said Tuesday that if the court does uphold the state’s law, he will introduce legislation to overturn that decision and grant the federal government sole control on immigration matters.

Mr. Schumer’s legislation would also overturn a 2011 Supreme Court case that upheld a separate Arizona law that requires all businesses in the state to check employees’ legal status using E-Verify, the federal government’s electronic verification system.

In that instance Congress specifically left open the chance for states to pass their own business licensing laws, and in a 5-3 ruling the justices upheld Arizona’s attempt.

Since Arizona passed its laws, other states have followed suit. Local enforcement laws have been adopted in a half-dozen states, though all have been challenged in court. Still states have adopted requirements that businesses use E-Verify.