Washington (CNN) The House of Representatives is investigating whether President Donald Trump lied to special counsel Robert Mueller in written answers he provided in the Russia investigation , the House's general counsel said in federal court Monday.

"Did the President lie? Was the President not truthful in his responses to the Mueller investigation?" House general counsel Douglas Letter told the US Court of Appeals for the District of Columbia Circuit about why the House now needs access to grand jury material Mueller collected in his investigation.

The House's arguments Monday draw new focus to whether Trump lied to Mueller, following public revelations at Roger Stone's trial this month

Former Trump deputy campaign chairman Rick Gates testified that Trump and Stone had talked about information that was coming that could help the campaign in mid-2016, at a time when Stone was attempting to get secret details about stolen Democratic documents WikiLeaks had.

Former Trump campaign chairman Paul Manafort also apparently told the Mueller grand jury what Trump's approach to WikiLeaks had been in 2016, according to the Mueller report.

But Trump told Mueller in his written statements he didn't recall discussing WikiLeaks with Stone.

The Gates testimony adds further significance to Congress' desire to see the redacted material.

The question of whether Trump obstructed justice, including potentially lying to Mueller, has for months been a part of the House Judiciary Committee's wider review of potential obstruction in the wake of the Mueller report. The House previously reviewed most of what Mueller had written in his final report, including parts kept from the public.

But the House hasn't been able to see what Manafort told the grand jury, which Mueller apparently described in his report. In the Mueller report, grand jury details are redacted related to a sentence describing Manafort speaking with Trump after WikiLeaks' first release, in July 2016.

Manafort's "situation shows so clearly that there is evidence, very sadly, that the President might have provided untruthful answers and this is a key part of the impeachment inquiry," Letter said Monday in the last words of his arguments to the three-judge appellate panel.

Judge Judith Rogers on Monday expressed skepticism about the Justice Department's reasoning for withholding the Manafort information from the House now.

"Why wouldn't the department favor giving this information because arguably it would show he did nothing wrong? The House would not want to return a charge where the evidence didn't support it," she said about the impeachment inquiry.

Rogers questioned the Justice Department attorney Mark Freeman in court harshly, at times even openly arguing with points he made.

Another judge on the panel, Thomas Griffith, also pelted Freeman with questions, reminding him how the courts have released grand jury information related to the President during past impeachment probes. But he then pressed the House too on exactly why it needed grand jury information. The third judge, Neomi Rao, whom Trump appointed, asked far fewer questions and at times focused on whether the courts should be involved in releasing information to the House that could influence an impeachment investigation.

In her first question for Freeman, Rao asked whether it would be inappropriate for the courts to take action, by releasing information to the House that could "interfere with impeachment." The impeachment inquiry "changes our involvement in this dispute," she said.

Griffith and Rao also expressed concern that the House could make public secret grand jury details it got.

"Recent history suggests some norms are not in place that were in place then," Griffith told the House general counsel, after the lawyer pointed out how Congress hadn't made public secret grand jury information it got during Watergate.

The court case revolves around what federal investigative information the House should be able to access during impeachment proceedings and what federal courts may do in a dispute between the House and the executive branch.

The appeals judges updated their approach to the case Monday night following the arguments, placing on the calendar another in-court round in January.

The hearing Monday morning specifically dealt with questions of whether the court can and should prevent the House from getting the details now, while other questions that go to the heart of the case, especially about the separation of powers, are still pending.

The panel of judges said Monday night that it would keep the House from seeing the grand jury materials "pending further order of the court."

The Justice Department has sought to keep the House from getting the secret grand jury information before the case is resolved, while the House seeks the grand jury details quickly.

The next round of arguments, about the merits of the case, will be January 3, per the circuit court.

While that date nears, Trump's willingness to give written answers to investigators -- and what he submitted to Mueller in 2018 -- may become more important in the impeachment probe.

In tweets about the Democrats' suggestion that he testify, Trump wrote Monday morning that House Speaker Nancy Pelosi "said I could do it in writing" and that he would "strongly consider it!"

Trump's responses to Mueller

House Judiciary Democrats asked Mueller at a summer hearing to confirm that Trump had denied to the special counsel that he or anyone on his campaign had discussed WikiLeaks with Stone. Rep. Mary Gay Scanlon, a Pennsylvania Democrat, read to Mueller Trump's written answer: "I do not recall discussing WikiLeaks with him, nor do I recall being aware of Mr. Stone having discussed WikiLeaks with individuals associated with my campaign."

"Is it fair then, that the President denied knowledge of himself or anyone else discussing WikiLeaks dumps with Mr. Stone?" Scanlon asked.

"Yes. Yes," Mueller replied.

This story has been updated with the scheduling of another court hearing.