WASHINGTON — The State Department has agreed to a conservative legal group’s request to question several current and former government officials about the creation of Hillary Clinton’s private email system.

The agreement filed late Friday with the U.S. District Court in Washington comes after a judge consented to allow the group Judicial Watch “limited discovery” to probe why Clinton relied on an email server in her New York home during her tenure as secretary of state.

Questions about the email system have bedeviled Clinton during her run for the Democratic presidential nomination.

If Judge Emmet G. Sullivan approves of Friday’s agreement, lawyers from Judicial Watch will be allowed to depose Clinton’s top aides, including former chief of staff Cheryl D. Mills, deputy chief of staff Huma Abedin and undersecretary Patrick F. Kennedy.

Also on the list to be questioned is Bryan Pagliano, the department employee who set up and maintained Clinton’s home-brew email system. Pagliano previously invoked his Fifth Amendment right in declining to answer questions from a congressional committee.

The FBI is investigating whether sensitive information that flowed through Clinton’s email server was mishandled. The inspectors general at the State Department and US intelligence agencies are separately investigating whether rules or laws were broken.

There are also at least 38 civil lawsuits, including one filed by the Associated Press, seeking copies of government records related to Clinton’s time as secretary of state from 2009 to 2013.

Critics of Clinton’s decision to rely on the private server have suggested it potentially made her communications more vulnerable to being stolen by hackers, including those working for foreign intelligence agencies.

In response to public records requests, the State Department has released more than 52,000 pages of her work-related emails, a small percentage of which have been withheld because they contain information considered sensitive to national security. Thousands of additional emails have been withheld by Clinton, whose lawyers say they contain personal messages unrelated to her government service.

Clinton has admitted on the campaign trail that her home-based email setup was a mistake, but she insists she never sent or received any documents that were marked classified at the time.