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Attorney General Eric Holder, just days after filing a federal lawsuit against Arizona's immigration law, on Sunday floated the possibility of filing another court challenge on racial profiling grounds.

The lawsuit filed Tuesday in U.S. District Court in Arizona claimed the state was infringing on federal immigration responsibilities and urged the judge to prevent the law from going into effect at the end of July. Despite some officials' claims that the law could lead to racial profiling, that concern was not cited as grounds for the suit.

However, Holder said on CBS' "Face the Nation" that the federal government was leading with its "strongest" argument in the suit filed Tuesday and would not rule out a second suit months down the road -- if the law ends up going into effect.

"It doesn't mean that if the law for whatever reason happened to go into effect, that six months from now, a year from now, we might not look at the impact the law has had ... and see whether or not there has been that racial profiling impact," Holder said. "If that was the case, we would have the tools and we would bring suit on that basis."

Holder, reacting to the firestorm of criticism from Republicans and border-state lawmakers, said the Justice Department decided to file the suit because Arizona's immigration law is "inconsistent" with federal policy and the U.S. Constitution. He said there's nothing to stop local jurisdictions and states from helping the government enforce immigration law, but described Arizona's law as contradictory to what the federal government is trying to accomplish.

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The law makes illegal immigration a state crime. It requires local law enforcement to question anyone they suspect of being an illegal immigrant on their immigration status -- provided they don't stop them for that reason alone.

Sen. Jon Kyl, R-Ariz., disputed Holder's characterization. Speaking on "Fox News Sunday," he said Arizona's law is trying to help, not hinder, the federal government's immigration efforts.

"It's not really a matter of preempting the federal law. It's simply the state of Arizona providing some additional law enforcement assistance for the federal government," Kyl said.

But Rep. Luis Gutierrez, D-Ill., suggested the Justice Department had more than enough legal basis on which to mount its lawsuit. Speaking on ABC's "This Week," he said that while the government is arguing that its policy preempts the state policy, the case can still be made that the law leads to "racial profiling and civil rights violations."