"Until we obtain operational control of our southern border and fully enforce current laws, we can't have a credible, substantive conversation on immigration reform," he added. "By enhancing the enforcement of our immigration laws, this ruling puts us on that path."

The Supreme Court said it is constitutional for Arizona to check the immigration status of people who are stopped by police for other reasons, a provision that opponents of the law saw as the most problematic.

The court did strike down other aspects of the law that allow for the arrest of illegal immigrants, prevented them from working and prevented employers from hiring illegal immigrants. The court held that this level of enforcement interfered with the federal government's primary enforcement role.

Quayle said it is "unfortunate" that these provisions were struck down and said Arizona put the law in place because the federal government is not meeting its requirements.

"The federal government has failed spectacularly in its duty to enforce immigration laws, and Arizona's law simply sought to fill the enforcement void left by this failure," he said.