The advocacy groups told a federal three-judge panel that using the data to verify whether voters are citizens amounts to a "systematic purging" of voting rolls that must be approved by the Justice Department.
Georgia is one of several states that needs federal approval before changing election policy because of a history of discriminatory voting practices.
Three Justice Department lawyers joined the debate Wednesday, arguing that Georgia officials should have cleared the checks with them first. But they cautioned against making sweeping changes less than two weeks before the Nov. 4 election.
Secretary of State Karen Handel's attorneys argued the checks were required by federal law and were an attempt to guarantee the integrity of the vote.
The judges said they will rule as soon as possible.
State attorney Dennis Dunn said the checks have so far flagged 4,538 voters, 3,821 of them newly registered, as noncitizens.
The fight centers on Jose Morales, a college student who became a U.S. citizen in November 2007 and registered to vote last month. He has twice received letters that warn him his name could be removed from voter rolls if he does not verify his citizenship.
The voting rights groups, including the American Civil Liberties Union and the Mexican American Legal Defense and Educational Fund, say the letters are a form of intimidation.