Complicating matters, this week the Department of Motor Vehicles called into question the data the state had provided. It said that although the report said 240,000 registered voters lacked a state-issued identification card, the real figure was probably closer to 80,000 because many had died or moved away.

In its letter, the Justice Department said that the new data — which contained no demographic breakdown — did not change its decision because the burden is on the state to prove that its change to election rules would not suppress minority voting. But it also noted that the state could ask the department to reconsider its decision on the basis of new information, once it re-examines the demographics.

The department also suggested that the voter registration data supplied by South Carolina might instead be too low because the state did not include “several categories of existing registered voters listed as inactive voters,” apparently a status conferred on people who failed to participate in several recent elections.

The South Carolina law also allowed several other forms of photographic identification to be used, such as military ID cards or passports, but the state supplied no data about how many registered voters who lack a driver’s license might have one of those.

Restrictions on voting and vote fraud have been an increasingly contentious topic of partisan dispute. Supporters — mostly Republicans — have portrayed voting fraud as rampant, and say restrictions are necessary to prevent the dilution of ballots cast by legitimate voters. Critics — mostly Democrats — contend that the restrictions are a veiled effort to suppress participation by legitimate voters who tend to favor their party’s candidates.

Documented cases of the sort of fraud that photo identification laws seek to limit — ineligible people showing up at the polls and casting ballots in person — have been few and isolated, although there is greater evidence that absentee ballot fraud has been used to attempt to alter the results of an election, including a 1997 mayoral election in Miami.

South Carolina’s current rules, enacted in 1988, allow people to vote by presenting a voter registration card and signing a document. The Justice Department letter said that while the state had justified adding the requirement to present photographic identification as a way to deter fraud, it did not submit “any evidence or instance” of “in-person voter impersonation” or some other kind of fraud that could be deterred by the new requirement.