The hearing centered on a Federal District Court’s ruling last month that the House should be given access to secret grand jury evidence from the Mueller investigation immediately, and whether enforcement of that ruling should be stayed while the Justice Department’s appeal is fully litigated.

Later on Monday, the appellate panel decided to keep a stay of the lower-court ruling in place “pending further order of the court,” while issuing an expedited briefing schedule with arguments set for Jan. 3.

If the judiciary keeps the stay in place — including for the likely appeals — House Democrats appear unlikely to receive the grand jury evidence before they decide whether to move forward with an impeachment vote.

Still, the argument underscored that they already have evidence calling into question the honesty of Mr. Trump’s responses from the Mueller report and the recently concluded trial of Mr. Trump’s longtime friend and informal adviser Roger J. Stone Jr.

Mr. Trump had refused to let the special counsel’s office interview him. But in his written responses, which were appended to the Mueller report, he denied that he was aware of any communications between his campaign and WikiLeaks.

House lawyers had suggested in a Sept. 30 filing that some of the materials they were seeking bore in on whether Mr. Trump lied about that subject. And on Monday, Douglas Letter , the general counsel for the House, told a federal appeals court panel that impeachment investigators had an “immense” need to swiftly see the grand jury evidence — redacted portions of the Mueller report, as well as the underlying testimony transcripts they came from.

“Was the president not truthful in his responses to the Mueller investigation?” Mr. Letter said, adding, “I believe the special counsel said the president had been untruthful in some of his answers.”