After President Trump made his groundless claim that he lost the popular vote in the 2016 election to Hillary Clinton only because millions of illegal ballots were cast, the White House appointed a panel to investigate claims of fraud. In June, its vice chairman and day-to-day leader, Kris Kobach, the Kansas secretary of state, asked officials in 50 states and the District of Columbia to voluntarily provide personal records about their voters, but was met with a bipartisan rebuke and lawsuits.

The issue in the Ohio case centers on an ambiguous and convoluted set of statutory provisions created by the National Voter Registration Act of 1993 and the Help America Vote Act of 2002. They require states to keep voter rolls up to date by deleting the registrations of voters who move away, but bar states from de-registering people simply because of voting inactivity.

Under Ohio’s process, if registered voters have sat out elections for two years, the state mails warnings to their addresses. If the recipients then do not cast ballots in the next two federal elections or have some other contact with elections officials in that time, the state purges them from the rolls.

The Obama-era Justice Department argued that before sending the warning, the state should have “reliable evidence” that a voter may have moved — such as registering a forwarding address at the post office. It said starting the process simply because people failed to vote risked illegally purging voters “based purely on inactivity rather than actual ineligibility.”

But the Trump-era Justice Department argued that Congress wanted states to make sure voter registration rolls were up to date in order to curb the risk of fraud, and that Ohio’s approach was a permissible means of doing that.

“Registrants are sent a notice because of that initial failure, but they are not removed unless they fail to respond and fail to vote for the additional period,” the new brief said.

Georgia uses a similar tactic for purging voter rolls, which is also the subject of litigation.

The new Supreme Court brief in the Ohio case was signed by Jeffrey B. Wall, the acting solicitor general, and John M. Gore, the acting assistant attorney general for the Justice Department’s civil rights division. It was not signed by any career attorneys in the civil rights division, unlike last year’s brief with the appeals court.