The Supreme Court announced Monday that it will hear a case on Arizona’s tough immigration-crackdown law, adding yet another contentious clash between the Obama administration and the states to the docket that already includes a challenge to the president’s new health care law.

At stake is whether Arizona and the half-dozen other states that followed its lead can have their own state and local police check the immigration status of those they suspect to be illegal immigrants, and whether states can require legal immigrants to carry their papers with them at all times.

Arguing that the federal government has failed to tackle illegal immigration, Arizona enacted its law in 2010 to try to make it more difficult for illegal immigrants to live and work in the state. Backers said they hoped the measure would push illegal immigrants out of Arizona, which they said would save the state hundreds of millions of dollars in education and prison costs and benefit payments.

“This case is not just about Arizona. It’s about every state grappling with the costs of illegal immigration,” said Arizona Gov. Jan Brewer, a Republican whose signature on the legislation turned her into a national leader on immigration issues. “Beyond the obvious safety issues, the fiscal burdens imposed upon Arizona by illegal immigration are daunting.”

The Obama administration challenged the law and won an order blocking key provisions in district and appeals courts. Arizona asked the Supreme Court to hear its appeal of those decisions.

The case marks the second major battle between the Obama administration and the states to reach the court this year. Last month, the court announced that the justices would hear the states’ challenge to the health care law.

In both cases, Paul D. Clement, who served as solicitor general for President George W. Bush, is arguing the states’ cases.

The Supreme Court said Justice Elena Kagan had recused herself from the decision to take the immigration case, suggesting she won’t be part of the hearing or final ruling.

She has come under fire from conservatives for not recusing herself from the health care case, since she was solicitor general for Mr. Obama from March 2009 through May 2010. She stopped taking part in cases in March 2010, when she learned that she was under consideration for the high court, in order to preserve her ability to take part in rulings as a justice.

The health care legislation was signed in March 2010, but emails show her colleagues began talking about a legal strategy as early as January, leaving one top Republican congressman to question the “two-month gap” in the record.

Arizona’s immigration law was enacted in April 2010, which suggests the Justice Department must have started laying out its legal strategy even before Mrs. Brewer signed the legislation.

At the White House, press secretary Jay Carney said the administration looks forward to laying out its case before the court.

Arizona’s law local enforcement provisions were matched by laws in Georgia, Indiana, South Carolina, Utah and Alabama. The Justice Department has sued to block enforcement in many of those states, while immigrant rights groups have sued to halt the others.

The Obama administration and its supporters say that only the federal government can set immigration policy and argue that any state whose enforcement conflicts with federal priorities must yield.

“While it is incredibly frustrating that many in Congress refuse to act on a solution to help fix our broken immigration system, immigration enforcement is unquestionably the responsibility of the federal government,” said Janet Murguia, president and CEO of the National Council of La Raza.

But lawyers who drafted the state legislation said the laws themselves complement, rather than clash with, federal law. They also said it is federal law as written by Congress, not the current administration’s priorities, that the courts should examine to determine whether states are interfering.

Arizona’s law had far-reaching consequences, including a boycott of the state’s businesses, led by the National Council of La Raza and other groups. The National Council of La Raza announced in September that it was calling off the boycott, though some other groups have said their calls remain in place.

Alabama’s law went further than Arizona’s by requiring public schools to check the legal status of students enrolled there — though it wouldn’t deny them the right to attend school, even if they were in the country illegally.

An appeals court has blocked that provision, and the state’s attorney general, Luther Strange, has suggested that lawmakers repeal that part of the law, along with another part that requires all legal immigrants and visitors to carry their papers with them. Federal law also requires legal immigrants to carry their proof of legal status.

Mrs. Murguia, president of the National Council of La Raza, said a court ruling striking down state laws could force Congress to take up a broad overhaul of immigration laws. Congress has tried major overhauls twice in the past five years, but each time it fell short as proponents couldn’t agree among themselves on what to include.

Arizona, which has been ground zero for illegal immigration over the past 15 years, has been a trailblazer in state action to try to combat it.

Earlier this year, the Supreme Court upheld another of those attempts that required businesses in the state to use E-Verify, the federal government’s voluntary system for checking employees’ Social Security numbers, to determine whether their new hires are legal workers.

In that case, the justices said a 1986 law specifically gave states the ability to write their own business-licensing schemes when it comes to immigration.

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