As part of the Russia inquiry, President Trump had given written answers to questions from Robert S. Mueller III.
House Democrats are exploring whether President Trump lied in his written answers to Robert S. Mueller III’s investigation, a lawyer for the House told a federal appeals court on Monday, raising the prospect of an additional basis for an article of impeachment.
The acknowledgment refocused attention on a quiet debate among Democrats about whether any impeachment of Mr. Trump should go beyond the Ukraine affair and also accuse him of obstructing the Russia investigation. Additional evidence, hidden in grand jury files, that Mr. Trump may have lied under oath to Mr. Mueller could bolster the case for an additional article of impeachment, Democratic aides said.
The House lawyer’s statement was also striking because it came shortly after Mr. Trump said he may also be willing to provide written answers about the Ukraine matter to impeachment investigators.
“Even though I did nothing wrong, and don’t like giving credibility to this No Due Process Hoax, I like the idea & will, in order to get Congress focused again, strongly consider it!” Mr. Trump wrote on Twitter.
His statement and the hearing, in a case over the House’s attempt to gain access to secret grand jury evidence gathered by Mr. Mueller, came as witnesses and lawmakers jostled for leverage before a new round of impeachment hearings scheduled to begin on Tuesday.
Kurt D. Volker, the former special envoy to Ukraine who will appear before lawmakers on Tuesday, planned to testify that he was out of the loop at key moments during Mr. Trump’s pressure campaign on Ukraine, according to an account of his prepared testimony.
Democrats conducting the inquiry added to their witness list an official at the American Embassy in Kyiv, David Holmes, who testified privately that he overheard Mr. Trump ask a top diplomat if Ukraine would move forward with investigations he sought. They also released transcripts of depositions by Mr. Holmes and David Hale, the under secretary of state for political affairs, that offered more details about the effort by Trump loyalists to pressure Ukraine for the investigations.
And House Republicans wrote to Senator Ron Johnson, Republican of Wisconsin, who attended the inauguration of Ukraine’s president this year, asking him to provide “any firsthand information you have about President Trump’s actions toward Ukraine.”
But the court hearing heightened attention on House Democrats’ longstanding suspicions about Mr. Trump’s responses to questions in the Russia investigation.
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.”
He was referring to congressional testimony in July when Mr. Mueller agreed with a lawmaker’s assertion that the president’s written responses “showed that he wasn’t always being truthful.”
Both the lawmaker in July and Mr. Letter on Monday were referring in particular to the question of whether Mr. Trump lied about his campaign’s advance knowledge of and contacts with WikiLeaks about its possession of hacked Democratic emails and plans to publish them.
Mr. Trump wrote that he was “not aware during the campaign of any communications” between “any one I understood to be a representative of WikiLeaks” and people associated with his campaign. Mr. Stone was convicted last week of lying to congressional investigators about his efforts to reach out to WikiLeaks and his discussions with the campaign.
“I do not recall discussing WikiLeaks with him,” Mr. Trump also wrote of Mr. Stone, “nor do I recall being aware of Mr. Stone having discussed WikiLeaks with individuals associated with my campaign.”
But the publicly available portions of the Mueller report suggest that evidence exists to the contrary. Several Trump aides, including Michael D. Cohen and Rick Gates, testified that they heard Mr. Trump discussing coming WikiLeaks releases over the phone.
And in October 2016 Stephen K. Bannon, the campaign chairman, wrote in an email that Mr. Stone had told the campaign “about potential future releases of damaging material” by WikiLeaks shortly before it began publishing more hacked emails.
Mr. Letter brought up redactions in the report associated with Mr. Stone and a redacted reference to an assertion by Paul Manafort, Mr. Trump’s former campaign chairman, to a grand jury.
“Manafort said that shortly after WikiLeaks’ July 22, 2016, released of hacked documents, he spoke to Trump [redacted]; Manafort recalled that Trump responded that Manafort should [redacted] keep Trump updated,” the Mueller report said, citing grand jury material as the reason for the redactions.
The report went on to suggest that House investigators may see Mr. Manafort’s grand jury testimony as potentially corroborating Mr. Gates’s account of Mr. Trump’s conversation with Mr. Stone about WikiLeaks.
“Deputy campaign manager Rick Gates said that Manafort was getting pressure about [redacted] information and that Manafort instructed Gates [redacted] status updates on upcoming releases,” the report said, citing an F.B.I. interview with Mr. Gates.
Mr. Letter told the court, “The Manafort situation shows so clearly that there is evidence, very sadly, that the president might have provided untruthful answers,” and added that it “might be part of an impeachment inquiry.”
The Mueller report cited additional evidence from Mr. Gates that Mr. Trump did have discussions about the content or timing of the future release of hacked emails.
For example, Mr. Gates also told investigators that about that same time, he was with Mr. Trump in a car to an airport when Mr. Trump received a call. After something that is redacted in the public version of the report, it recounts that after Mr. Trump hung up, he told Mr. Gates “that more releases of damaging information would be coming,” the report said.
Attorney General William P. Barr permitted the House Judiciary Committee to see most of the Mueller report, including portions that are redacted from the public version because they pertained to continuing cases, but he has refused to let it see material that is subject to secrecy rules because it was presented to a grand jury.
In July, House lawmakers petitioned the chief judge of the Federal District Court for the District of Columbia, Beryl A. Howell, for an order allowing them to gain access to that material too. Their court filings in that matter were the first time that the House formally pronounced itself engaged in an impeachment inquiry; there is precedent, including in Watergate, permitting the House to get grand jury information for impeachment proceedings.
Judge Howell ruled in October that the Judiciary Committee should be permitted to see the grand jury material in the report and its underlying basis. But the Justice Department appealed that ruling, arguing that the Watergate precedent was wrong and Congress had no right to see grand jury evidence even for impeachment purposes.
The appeals court panel includes Judge Neomi Rao, a former Trump White House official whom he recently appointed to the bench; Judge Judith W. Rogers, a 1994 appointee of President Bill Clinton; and Thomas B. Griffith, a 2005 appointee of President George W. Bush.