A federal judge has reopened an open-records case trying to pry loose some of former Secretary of State Hillary Rodham Clinton’s emails, marking the first time a court has taken action on the email scandal. Judge Reggie B. Walton agreed Friday to a joint request by the State Department and Judicial Watch, which sued in 2012 to get a look at some of Mrs. Clinton’s documents concerning a public relations push. Both sides agreed that the revelation that Mrs. Clinton had kept her own email server separate from the government, and exclusively used her own email account created on that server, meant that she had shielded her messages from valid open-records requests.

Now that she has belatedly turned some emails over, the government offered — and Judge Walton confirmed in his ruling — that the agency should search them all to see whether any should have been released to Judicial Watch. “This is the first case that’s been reopened,” Tom Fitton, president of Judicial Watch, said Friday. “It’s a significant development. It points to the fraud by this administration and Mrs. Clinton.”

Judicial Watch has filed a series of open-records requests seeking State Department emails and, when the administration failed to comply, has gone to court to force them. Just last week Judicial Watch filed a new batch of eight lawsuits trying to shake loose some of the secret emails, and said that was just the first round.

The State Department said it doesn’t comment on open-records lawsuits.

Publicly, the department has struggled to handle the inquiries over Mrs. Clinton’s emails. Officials didn’t acknowledge that there were missing emails until prodded by the House committee investigating the 2012 terrorist attack on the U.S. diplomatic post in Benghazi, Libya. After that prod, the department asked Mrs. Clinton to turn over emails that contained government business. She provided about 30,000 emails, but said she discarded another 32,000 she deemed weren’t government business, and then wiped the server. She has refused requests by the Benghazi inquiry chairman, Rep. Trey Gowdy, South Carolina Republican, to turn the server over to a neutral third party.

On Friday, Mr. Gowdy released an interim report detailing his first year of investigation, citing “obstacles and frustrations” in dealing with the administration. He said they have talked with new witnesses who hadn’t been interviewed by any other Benghazi probe, and had unearthed documents that haven’t been part of other investigations. But he said Mrs. Clinton’s emails remain a large question mark, and the State Department still hasn’t turned over emails from her senior staff.

“The State Department has told the committee that it cannot certify that it has turned over all documents responsive to the committee’s request regarding the former secretary’s emails,” Mr. Gowdy said in his report.

Mr. Gowdy also hinted that Congress’s investigative powers may be limited when it comes to trying to force a president and his team to come clean.

“The legislative branch’s constitutional toolbox seems inadequate to uphold our task in seeking the truth,” Mr. Gowdy said, pointing to the administration’s unwillingness to serve subpoenas on itself, neutering much of Congress’s investigative power.

Mr. Fitton said that’s why his group’s lawsuits are so critical, saying Congress’s hands are tied and the Justice Department hasn’t committed to conduct an investigation of another part of the Obama administration.

“It’s going to be independent actions by JW at this point,” Mr. Fitton said. “This is how anything is going to break loose.”