A federal judge declined Thursday to impose a gag order that would bar President Trump from talking about a former Senate staffer accused of lying to investigators probing the leak of confidential information.

U.S. District Judge Ketanji Brown Jackson said attorneys for James Wolfe had not proven that Mr. Trump’s comments accusing him of leaking sensitive material would prejudice the case.

“The defendant’s right to a trial by an impartial jury is not hindered just because of misleading or inaccurate statements,” she said.

Mr. Wolfe, who oversaw the transmission of sensitive documents for the Senate Select Intelligence Committee, is accused of lying about his personal relationships with reporters to FBI agents.

He made those statements to authorities probing committee leaks about former Trump campaign aide Carter Page, but he has not been charged with actually leaking information.

However, that has not stopped Mr. Trump from calling Mr. Wolfe a “very important leaker.”

“I’m a big, big believer in the freedom of the press,” the president told reporters in June, just after Mr. Wolfe’s arrest. “But I’m also a believer in classified information. It has to remain classified.”

Attorneys for Mr. Wolfe have claimed those comments have compromised his right to a fair trial. They told Judge Brown that if Mr. Trump continues to comment on the case, it would make it nearly impossible for jurors to be impartial.

“The concern is who this person is — this president — and that he’s commenting on the case in a factually inaccurate way,” said Benjamin Klubes, who is representing Mr. Wolfe.

But Judge Jackson was unmoved. She noted that people, such as cable television pundits, make misleading and inaccurate claims about court cases all the time.

“What you have asked to me do is police the discussion between now and the trial,” she said.

Winning the gag order fight was a long shot for Mr. Wolfe’s attorneys. They acknowledged the slim chances of having their requested granted, admitting that it was “unprecedented.”

At a hearing earlier this month, Judge Jackson seemed skeptical of their arguments because, typically, orders only apply to the parties in the case.

Defense counsel attempted to argue that Mr. Trump is, in fact, a party, saying the president oversees all branches of government, including the Justice Department, which is prosecuting Mr. Wolfe. But Judge Jackson was unmoved by the argument, noting the Justice Department has accused Mr. Wolfe of a crime.

Mr. Wolfe’s attorneys declined to comment on Judge Jackson’s ruling upon leaving the courthouse.

Laura Ingersoll, who among the team prosecuting Mr. Wolfe, made a very brief argument, merely expressing the government’s confidence that the court will be able to prevent any potential prejudice from influencing the jury.

Mr. Wolfe faces three counts of lying to the FBI. He could face up to five years in prison and $250,000 fine for each charge.

A 30-year Senate employee, Mr. Wolfe is accused of lying when he denied having any personal relationships with reporters. Federal prosecutors say he had a three-year romantic relationship with New York Times reporter Ali Watkins. The Justice Department has seized communications from Ms. Watkins as part of its investigation.

An indictment unsealed last month says Mr. Wolfe, 58, started a relationship an unnamed reporter. But it is widely believed that reporter is the 26-year-old Ms. Watkins, who has admitted a relationship with Mr. Wolfe. She has denied using him as a source for her articles, a claim that also has had doubt cast upon it.

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