The United States attorney’s office in Alexandria, Va., referred questions to the Justice Department in Washington. The department did not immediately respond to requests for comment on Wednesday.

The ruling on Tuesday addressed only Mr. Snowden’s liability for breaching his agreements with the intelligence agencies, not how much the government would seek to recover or how it would do so. The lawsuit against Mr. Snowden also named his publisher, Macmillan, as a defendant, but prosecutors have said they were only seeking to prevent the company from paying royalties to Mr. Snowden that should instead be turned over to the federal government.

Mr. Snowden has been celebrated as a whistle-blower by advocates for privacy and civil liberties but denounced as a traitor by some national security officials. His disclosure in 2013 prompted a worldwide debate about the reach of modern government-surveillance programs.

It also prompted reforms. In 2015, Congress ended the N.S.A.’s collection of logs of Americans’ phone records. The Trump administration asked Congress in August to reauthorize an alternative surveillance system.

In 2013, federal prosecutors charged Mr. Snowden with violations of the Espionage Act, which outlaws the disclosure of potentially harmful national security information to someone not authorized to receive it.

Mr. Snowden, however, has been living as a fugitive in Russia and the case has not proceeded. He has said that paid lectures are one of his main forms of income there.

Consenting to prepublication review is a routine part of gaining a security clearance.

But Tuesday’s ruling came as groups, including the Knight First Amendment Institute at Columbia University and American Civil Liberties Union, are challenging the process, arguing in a lawsuit filed in April by former military and intelligence officials that it is “dysfunctional” and unjustifiably restrictive of free-speech and due-process rights.