Rick Gates, one of the individuals indicted by special counsel Robert Mueller’s investigation into Russian election meddling, is facing new questions in federal court over his role in a recent fundraiser hosted by Republican lobbyist Jack Burkman.

The federal judge presiding over the criminal cases against President Trump’s former campaign associates issued a ruling Friday ordering Mr. Gates to explain how his comments in a prerecorded video played during the event didn’t violate a previously imposed gag-order preventing him from publicly discussing the case.

“Thank you to Jack Burkman for hosting the fundraiser, for believing in the cause and for ensuring that supporters from across the United States hear our message and stand with us,” Mr. Gates said in a video played for attendees including journalists during Tuesday’s fundraiser in Arlington, Virginia.

“As you may be aware, there is a gag order in the case, so I am not able to talk specifically about the case. However, I can say because of you we will have the resources to fight,” Mr. Gates said.

The video was played during an event that had been billed as a fundraiser for former Trump associates charged in connection with the president’s 2016 campaign, and U.S. District Judge Amy Berman Jackson wants Mr. Gates to detail the extent of his involvement.

The order issued in D.C. federal court Friday gives Mr. Gates until Wednesday, Dec. 27, to “show cause” why his personal participation in the video didn’t violate the Nov. 8 gag order, according to the case docket.

Mr. Gates must also explain his relationship with Mr. Burkman, who reportedly called the case against him “very unfair,” the court order said.

“The Court emphasizes that it is not intimating that the creation of a legal defense fund or the expression of personal views by third parties not acting at the behest of the defense would violate its order,” the order said.

An attorney for Mr. Gates did not immediately return an email seeking comment.

“This is a very systematic, deliberate and probably political effort and order on the part of the judge to take away Rick’s First Amendment rights and my First Amendment rights,” Mr. Burkmantold Bloomberg. “When you reach the point where we have to be afraid to host an event at a Holiday Inn and speak our minds, Joseph Stalin might as well rule the United States.”

“Despite the presence of what I believe to be tyranny, we will continue to help Rick and we will probably hold other fundraisers,” Mr. Burkman said.

Mr. Gates is a political consultant and previously worked on Mr. Trump’s successful White House run directly under Paul Manafort, the president’s former campaign manager. A grand jury convened by Mr. Mueller, a former FBI director leading the Department of Justice’s investigation into the race, unsealed charges in October against both Mr. Gates and Mr. Manafort including counts of conspiracy against the U.S., making false statements, money laundering and failing to register as foreign agents. Both pleaded not guilty, and their cases are currently scheduled to go to trial in 2018.

Mr. Mueller’s office and four congressional committees are currently investigating Russia’s involvement in last year’s White House race, including possible collusion between the White House and Kremlin. Russian President Vladimir Putin has denied interfering in the 2016 election, and Mr. Trump has denied colluding with Russian operatives.