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Secretary of State Hillary Clinton on Sunday said that Arizona's immigration law invites racial profiling, in one of the toughest statements made to date by an Obama Cabinet member about the controversial state policy that has revived national debate about illegal immigration.

Clinton said the law was "clearly a result of frustration" in the state over the difficulty of securing the border and stopping the flow of illegal immigration. But she said immigration law enforcement is the purview of the federal government, not the states, and condemned the policy itself as flawed.

"It is written so broadly that if you were visiting in Arizona and you had an accent and you were a citizen from my state of New York, you could be subjected to the kind of inquiry that ... this law permits," she told NBC's "Meet the Press."

Asked whether the law invites racial profiling, she said: "I don't think there's any doubt about that."

The Arizona policy would make illegal immigration a state crime and empower local law enforcement to question people about their immigration status and require them to show documentation or face arrest.

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"If you're a legal resident, you still have to carry papers -- well, how is a law enforcement official supposed to know?" Clinton said.

Arizona Gov. Jan Brewer, though, just signed a package of changes to the law aimed at tempering concerns that it would lead to profiling. The changes would restrict police from basing their questioning on race or ethnicity.

"These new statements make it crystal clear and undeniable that racial profiling is illegal, and will not be tolerated in Arizona," Brewer said in a written statement.

Arizona officials have firmly defended the new law, saying it's needed to enforce an out-of-control border problem and reduce crime.

Rep. Mike Pence, R-Ind., said on "Meet the Press" that federal officials should tone down their criticism of Arizona lawmakers.

"I don't know if this law if perfect, but I do know that it is wrong for officials in this government to throw stones at the people of Arizona as they're trying to re-assert the rule of law," he said.

President Obama and other top officials in the administration have criticized the law as misguided.

Attorney General Eric Holder said Tuesday that the Department of Justice is reviewing the policy and could consider a court challenge.

Clinton would not say Sunday whether she thinks the law would hold up in court.