Washington — Lawyers for House Democrats and President Trump were back in federal court on Tuesday. But this time, they were arguing for the same outcome: They want a lawsuit filed against them to be thrown out.

Charles Kupperman, Mr. Trump's former deputy national security adviser, sued both parties in October after he was subpoenaed by the House to testify in the impeachment inquiry but ordered by the White House not to appear.

The White House claims that the president's senior officials have "absolute immunity" from congressional subpoenas. That stance led more than a dozen current or former Trump officials to refuse subpoenas related to the impeachment process of the president.

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House Democrats, however, withdrew their demand for his testimony last month, citing the length of time it would take to litigate the case. Without Kupperman's testimony, the House started the formal impeachment process on Tuesday, after weeks of hearings with more than a dozen other witnesses. In court, House lawyers said Democrats will neither hold Kupperman in contempt nor attempt to subpoena him again.

Nevertheless, Kupperman has pushed ahead with his lawsuit, citing fears of being held in contempt of Congress and violating his oath of office.

Kupperman's attorney, Charles Cooper, said he trusts that House lawyers won't hold Kupperman in contempt for not testifying — but he doesn't trust the House members themselves. Cooper said many House Democrats have made "naked and completely contrary statements" on this issue. The House Intelligence Committee used Kupperman's refusal to testify as evidence of obstruction of justice in its impeachment report.

House Intelligence Chairman Adam Schiff, left, and House Speaker Nancy Pelosi stand behind House Judiciary Chairman Jerry Nadler to deliver a press conference July 24, 2019. Andrew Caballero-Reynolds

House lawyers, however, say the case is "moot" because of the current status of the impeachment inquiry. The Trump administration, on the other hand, opposes Kupperman's testimony "pursuant to the president's invocation of Dr. Kupperman's absolute immunity from testimonial compulsion," lawyers explained in separate court filings.

Kupperman's attorney also represents John Bolton, Mr. Trump's former national security adviser. Both ex-officials have made clear that they are willing to testify before the House committees, but the House hasn't scheduled any more witnesses.

In a separate subpoena case involving former White House Counsel Don McGahn, another federal judge rejected the White House's "absolute immunity" claim.

"Executive branch officials are not absolutely immune from compulsory congressional process ... even if the President expressly directs such officials' non-compliance," wrote Judge Ketanji Brown Jackson. "The primary takeaway from the past 250 years of recorded American history is that presidents are not kings."

That decision is being appealed by the Justice Department, which represents McGahn.