The rebuff is a victory for the Obama administration and voting- and minority-rights groups that battled the two states in court. It leaves intact a decision by a U.S. agency that blocked the states from requiring proof of citizenship for voters in federal elections.

It's the second high court defeat on the issue for Arizona. The state has a law that requires evidence of citizenship, but the Supreme Court ruled in 2013 that it couldn't be enforced when people use a standard registration document known as the "federal form" to register to vote for Congress and the president.

That 7-2 ruling left open the possibility that Arizona could impose its requirements through a different avenue.