President Donald Trump has formally invoked executive privilege in the court fight over his management of the John F. Kennedy Center for the Performing Arts, NBC News and the Washington Examiner reported Thursday.

In a court declaration filed Wednesday, according to the court docket, White House lawyer Josh Hoyt said that at "the direction of the President," he was "formally invoking the presidential communications privilege" over information, documents and communications sought by Rep. Joyce Beatty, D-Ohio, NBC reported. The privilege covers material "shared between the President, his advisors (government and non-government), and Kennedy Center staff, pertaining to the management and operation" of the center, Hoyt wrote, according to both outlets.

Beatty, an ex officio member of the center's board, sued over Trump's push to add his name to the building and the plan to close the center for two years of renovations. She has been seeking more details about Trump's role, NBC reported.

The Justice Department filed Hoyt's declaration with a response asking the court to deny Beatty's motion to compel the information, calling it a "fishing expedition" that raises "obvious separation-of-powers concerns," the Examiner reported. Beatty's lawyers filed that motion after lawyers for Kennedy Center Executive Director Matt Floca invoked the privilege during his testimony, the Examiner said.

"Donald Trump appointed himself as chair of the non-profit board of the Kennedy Center, and is now trying to shield his management by improperly invoking executive privilege," Beatty's lawyers, Norm Eisen and Nathaniel Zelinsky, said in a statement quoted by both outlets. "This kind of cover-up is a direct assault on the rule of law."

In an Oct. 6 filing, Beatty's attorneys argued there were no grounds for the privilege because Trump is a defendant as the board's chairman, not as president, NBC reported. The court can now grant Beatty's motion or side with the administration and let the privilege block the records, the Examiner said.

What we know: Trump formally invoked executive privilege, and the Justice Department asked the court to deny Beatty's request for the records.
What we don't: How the judge will rule on the privilege claim, or when.