The United States Supreme Court on Monday struck down most of Arizona’s controversial SB 1070 immigration law, but upheld that police could be required to inquire about immigration status when they stop suspects.

In a 5-4 ruling (PDF), the court said that federal laws preempted most of the Arizona law.

A provision that required police to check the immigration status of people that they stop was upheld, but the court left open the possibility that it could be challenged later.

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“Today’s decision by the Supreme Court is a victory for the rule of law,” Arizona Gov. Jan Brewer (R) said in a statement. “It’s also a victory for the 10th Amendment and all Americans who believe it is a responsibility of states to defend their citizens. After more than two years of legal challenges, the heart of SB 1070 can be implemented in accordance with the U.S. Constitution.”

Georgetown Law professor David Cole told CNN that the decision was “almost a total victory for the Obama administration.”

It’s not yet clear what the ruling means for states like Alabama and Georgia that passed similar laws based on Arizona’s example.

Update (11:30 a.m. ET): Senate Majority Leader Harry Reid (D-NV) praised the Supreme Court for striking down most of the Arizona law.

“With three out of the four provisions being struck down, the ruling shows that the Obama administration was right to challenge this law, which was not just ill-advised but also unconstitutional,” Reid said in a statement.

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“Looking ahead to the immigration debate, it is disturbing that Mitt Romney called the unconstitutional Arizona law a ‘model’ for immigration reform. Laws that legalize discrimination are not compatible with our nation’s ideals and traditions of equal rights, and the idea that such an unconstitutional law should serve as a ‘model’ for national reform is far outside the American mainstream.”

Sen. Chuck Schumer (D-NY) said the ruling was “as strong a repudiation of the Arizona law as one could expect given that the law has not been implemented yet.”

“This decision tells us that states cannot take the law into their own hands and makes it clear that the only real solution to immigration reform is a comprehensive federal law,” Schumer noted. “The decision should importune Republicans and Democrats to work together on this issue in a bipartisan way.”

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Update (1:00 p.m. ET): President Barack Obama has indicated that he is “pleased” with the court’s decision.

“At the same time, I remain concerned about the practical impact of the remaining provision of the Arizona law that requires local law enforcement officials to check the immigration status of anyone they even suspect to be here illegally,” the president said in a statement. “No American should ever live under a cloud of suspicion just because of what they look like. Going forward, we must ensure that Arizona law enforcement officials do not enforce this law in a manner that undermines the civil rights of Americans, as the Court’s decision recognizes.”

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For his part, presumptive Republican presidential nominee Mitt Romney used the opportunity to attack his opponent.

“President Obama has failed to provide any leadership on immigration. This represents yet another broken promise by this President,” Romney said. “I believe that each state has the duty–and the right–to secure our borders and preserve the rule of law, particularly when the federal government has failed to meet its responsibilities.”