The unsigned order said a federal judge should not have changed election rules so close to Election Day, citing the court’s precedent against late changes. The justices said the lower court had not shown a sufficient reason to depart from that principle.

Justice Ketanji Brown Jackson was the lone dissenter. She said she would have left in place the federal court order, which she described as necessary to ensure voters receive accurate information about the state’s election procedures.

The dispute stems from a New Hampshire law passed in April that removed student IDs from the list of documents election officials accept when voters request ballots. A voting-rights group, the Coalition for Open Democracy, challenged the law, arguing it burdened voting rights and discriminated against young voters.

U.S. District Judge Joseph Laplante declined to block the law itself. But on Oct. 2, he paused guidance from Republican Secretary of State David Scanlan that barred student IDs for any purpose in the ballot process. Laplante said the guidance went beyond the law, which prohibited student IDs as a primary form of identification.

Another state-law provision allows voters to establish identity through other evidence that makes it more likely than not that they are who they claim to be. Under Laplante’s order, election officials could have considered student IDs under that provision. The Supreme Court’s action prevents that option for the November election.

The ruling comes as New Hampshire voters prepare to choose between Republican former Sen. John E. Sununu and Democratic Rep. Chris Pappas in a closely watched Senate race. The seat is held by retiring Democratic Sen. Jeanne Shaheen, and the contest could affect which party controls the chamber.