“Congress . . . confronted a situation in which 40 percent of eligible voters were not registered, because state procedures and burdens were standing as an obstacle, a barrier in the direct line of accountability between individual citizens and their federal government,” Millett said.

The federal law requires would-be voters to sign a statement that they meet the voter eligibility requirements, which include U.S. citizenship. No other proof of citizenship is required, under the federal law.

“So it’s under oath, big deal,” Justice Antonin Scalia said dismissively, adding later: “This is proof? It’s not proof at all.”

Arizona’s Proposition 200 added the requirement that voter registration applicants include documentary proof of citizenship, such as a driver’s license, passport or birth certificate. State officials argue the evidence is necessary to support the simple signature required by the federal law.

“It’s extremely inadequate,” Arizona Attorney General Thomas Horne said of the federal signature requirement. “It’s essentially an honor system. It does not do the job.”

Opponents of the Arizona law counter that allowing states to layer on additional documentary requirements would thwart the purpose of the federal law.

“The whole point of this is to come forward with a federal form that streamlines the process of registration,” Deputy Solicitor General Sri Srinivasan said.

Justice Clarence Thomas, as is his custom, was the only one of the nine Supreme Court justices to remain silent for the entire oral argument.

A decision is expected by the end of June.