Writing for the majority, Justice Anthony Kennedy said sections of the Arizona law that make it a state misdemeanor to fail to comply with federal alien-registration requirements or to seek or engage in work without proper authorization both intrude on federal rights in "a field in which Congress has left no room for states to regulate."

Also overturned as "an obstacle to federal law" was a section that authorized state and local law enforcement to arrest a person without a warrant if the officer "has probable cause to believe" that the person "has committed any public offense that makes the person removable from the United States."

But because of certain limitations on the immigration checks, Kennedy said, "The mandatory nature of the status checks does not interfere with the federal immigration scheme."

These limitations include a stipulation that anyone with a valid Arizona driver's license or similar identification cannot be presumed an illegal alien; a ban on officers' consideration of race, color or national origin, except as allowed by law; and a requirement that the law be "implemented in a manner consistent with federal law regulating immigration, protecting the civil rights of all persons and respecting the privileges and immunities of United States citizens."

Joining Kennedy in the majority opinion were Chief Justice John Roberts and Justices Ruth Bader Ginsburg, Stephen Breyer and Sonia Sotomayor. Justices Antonin Scalia, Clarence Thomas and Samuel Alito each issued separate dissenting opinions. Justice Elena Kagan did not participate in the case or join in the decision because earlier she had recused herself.

Scalia said he believed the court should have upheld the entire law.

"Today's opinion ... deprives states of what most would consider the defining characteristic of sovereignty: the power to exclude from the sovereign's territory people who have no right to be there," he wrote. "Neither the Constitution itself nor even any law passed by Congress supports this result."

Thomas said he reached the same conclusion but not for the reasons outlined by Scalia. "There is no conflict between the 'ordinary meaning' of the relevant federal laws and that of the four provisions of the Arizona law at issue here," he wrote.

Six states have passed legislation modeled on Arizona's 2010 law and another 20 have considered doing so. Catholic leaders in Arizona and elsewhere had urged that the law be overturned, calling instead for a federal comprehensive immigration reform law as a way of dealing with immigration-related problems at a national level instead of state-by-state.

A brief filed by the U.S. Conference of Catholic Bishops -- along with the Evangelical Lutheran Church in America, Lutheran Immigration and Refugee Service and the stated clerk of the general assembly of the Presbyterian Church -- notes the churches' teaching on family unity and the government's interest in having immigration policies enable families to stay together.

It also said such state laws pose "a serious threat to religious liberty." Churches have a moral and religious duty to help all in need, it noted. And S.B. 1070 and similar laws "threaten this Catholic mission to provide food, shelter and other care to all." It added that by criminalizing the act of aiding undocumented immigrants, such laws also burden religious liberty, the brief said.

"A patchwork set of state 'harboring' regulations like S.B. 1070's would seriously threaten the Catholic Church's mission to serve all in need," it said. "The United States' effort to establish a single set of immigration laws thus constitutes a sound federal objective that this court should particularly respect."