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“After more than two years of legal challenges, the heart of SB 1070 can now be implemented in accordance with the U.S. Constitution,” she said.

The law required police to check immigration status of those they encountered whom they had reasonable suspicion were in the country illegally, and required that they contact federal immigration authorities to give them a chance to put the individuals in deportation proceedings.

The law also imposed state penalties on illegal immigrants who applied for jobs.

The Obama administration sued and lower courts stayed both of those parts of the law, and Mrs. Brewer appealed.

In the intervening two years a handful of other states moved ahead with their own crackdown laws, while other localities actually went the other direction to codify so-called sanctuary-city policies that discouraged police from reporting illegal immigrants to federal authorities.

Mr. Obama’s administration sued to stop the state crackdown laws but has not taken action against the sanctuary city policies.

During the debate over SB 1070, Mr. Obama and Attorney General Eric H. Holder Jr. both criticized the law as opening up the chance for racial profiling. But when they sued, they didn’t make that argument, instead confining their challenge to issues of federal versus state power.

The racial profiling challenge could still come later, though, as the law begins to be enforced — something Mrs. Brewer said she expects.

“Our critics are already preparing new litigation tactics in response to their loss at the Supreme Court, and undoubtedly will allege inequities in the implementation of the law,” she said. “As I said two years ago on the day I signed SB 1070 into law: ‘We cannot give them that chance. We must use this new tool wisely, and fight for our safety with the honor Arizona deserves.’”

Last week Mrs. Brewer issued an executive order asking that training materials be distributed to all police to refresh them on what constitutes reasonable suspicion for a stop. Race or ethnicity alone is not enough to meet the threshold.

Still to be seen is whether Thursday’s ruling opens the floodgates on other states to follow suit.

In 2011 the court upheld an earlier Arizona law that required all businesses in the state to use E-Verify, the voluntary electronic system the federal government makes available for businesses to make sure their new hires are legal workers.

After Arizona, a series of other states passed similar E-Verify laws, but that pace slackened in 2012, according to a study by ImmigrationWorks USA, which pushes for a broad national legalization solution to illegal immigration.

Sen. Charles E. Schumer, New York Democrat and chairman of the Senate’s subcommittee overseeing immigration, said before the Supreme Court’s oral arguments in April that he would try to pass a law undoing both this year’s decision and a 2010 ruling by the court that allowed states to require businesses to use E-Verify, the electronic worker verification system.