CNN  — 

A federal judge hearing arguments in a potentially critical impeachment inquiry case wants to hear from lawyers for the Trump White House, the House of Representatives and from impeachment witness Charles Kupperman on Thursday after Kupperman filed a lawsuit asking the federal court to decide whether he would need to testify.

Kupperman’s House testimony had been set for Monday, but Kupperman didn’t show up, citing White House and Justice Department reasoning that he was immune from testifying because of his previous work on the National Security Council.

Leon will meet the parties in court at 3 p.m. on Thursday, “due to the time-sensitive nature of the issues raised in this case,” Judge Richard Leon of the DC District Court wrote Monday night.

Kupperman, who served until last month as deputy national security adviser at the White House, was listening in on the July 25 phone call when, according to a White House transcript, Trump pressed Ukrainian President Volodymyr Zelensky to investigate former Vice President Joe Biden.

Kupperman’s lawsuit raises additional questions about possible testimony from former national security adviser John Bolton, as Kupperman’s lawyer Charles Cooper also represents Bolton.

“Plaintiff is faced with irreconcilable commands by the Legislative and Executive Branches of the Government and, accordingly, seeks a declaratory judgment from this Court as to whether he is lawfully obliged to comply with a subpoena issued by the House Defendants demanding his testimony ‘(p)ursuant to the House of Representatives’ impeachment inquiry,’ or he is lawfully obliged to abide by the assertion of immunity from congressional process made by the President in connection with the testimony sought from Plaintiff,” the lawsuit states.

Kupperman’s lawsuit includes a copy of a letter that White House counsel Pat Cipollone sent to Cooper directing Kupperman not to comply with the subpoena and maintaining that he would be protected by “constitutional immunity.”

Trump has slammed officials who have implicated him, such as the US’ top diplomat in Ukraine, Bill Taylor, who testified earlier this month that he had been told Trump would withhold military aid to Ukraine until it publicly declared investigations would be launched that could help his reelection chances, according to a copy of Taylor’s opening statement obtained by CNN.

House Democratic leaders announced earlier Monday that the full House will vote Thursday to formalize the procedures of the impeachment inquiry.

The vote signals a shift into the next stage of the investigation following several weeks of closed-door depositions, as Democrats said the resolution would establish rules for public hearings, provide due process rights for the White House and allow information to be transferred to the committee that would ultimately consider the articles of impeachment.

CNN’s Jeremy Herb, Lauren Fox, Manu Raju, Mary Kay Mallonee, Adam Levine and Caroline Kelly contributed to this report.