The lawsuit was brought by the conservative advocacy group
Abedin was given special permission to work for the Clinton Foundation and an outside consulting firm at the same time she was on the State Department payroll.
The State Department argued that the questioning was unnecessary after Clinton turned over tens of thousands of emails that had gone through her private server. The State Department has released them to the public in monthly batches since mid-2015.
But U.S. District Judge Emmet G. Sullivan was unconvinced.
On Tuesday, he ruled that Judicial Watch should proceed with a "narrowly tailored" discovery involving the questioning of Clinton aides.
The judge also is considering whether Clinton should be compelled to turn over all the emails that went through her private server, not just those that she and her lawyers self-selected as involving government business.
"The court-ordered discovery will help determine why the State Department and Mrs. Clinton, even despite receiving numerous [open records] requests, kept the record system secret for years," Tom Fitton, president of Judicial Watch, said in a statement.
The initial round of questioning will not include Clinton or Abedin, but the judge left open the possibility that they could ultimately be called to the stand.
"It may happen that [Clinton's] testimony is necessary for the court to resolve the legal issues about her undocumented email practices," Fitton's statement said.
State Department lawyers had argued in court that the testimony was unnecessary because the government had already searched through the emails turned over by Clinton for records related to Abedin's employment.
Judicial Watch's complaint that Clinton and Abedin "self-selected" their work emails "ignores the fact that federal employees routinely manage their email and 'self-select' their work-related messages when they, quite permissibly, designate and delete personal emails from their government email accounts," they wrote.
Sullivan issued his ruling from the bench Tuesday, where he said questions about how the State Department handled Clinton's email server have created "at least a 'reasonable suspicion'" that open-records laws were violated, according to a report in the Washington Post.
"This case is about the public's right to know," the judge said.
The lawsuit is separate from an ongoing FBI investigation into whether classified material was improperly sent and received through the unprotected computer server in the Clinton home.
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