In his first question-and-answer session with reporters since becoming Acting Attorney General last November, Matthew Whitaker on Monday announced that Special Counsel Robert Mueller's Russia investigation is “close to being completed."

Whitaker's remarks came just days after Mueller ordered the dramatic predawn arrest of former Trump adviser Roger Stone on charges he allegedly lied to Congress and directed another witness to do the same.

"I’ve been fully briefed, and I look forward to Mueller delivering the final report," Whitaker said. “Right now, the investigation is, I think, close to being completed.”

In response, House Intelligence Committee Chairman Adam Schiff, D-Calif., tweeted that Whitaker's remark was inappropriate.

"While the probe is ongoing, Mueller can speak for himself," Schiff wrote, after asserting that Whitaker should have recused himself from overseeing the Russia probe in part because of his past comments favoring limits on Mueller's authority. Whitaker has also attracted scrutiny for earning nearly $1 million from a secretive right-leaning nonprofit prior to joining the Justice Department.

Earlier this month, Trump’s legal team pushed back on the suggestion the White House could seek to keep parts of Mueller's final report under wraps.

“We prefer that as much of the report as possible is public,” Trump attorney Rudy Giuliani told Fox News. "We believe a selective release would be problematic.”

In his remarks to reporters Monday, Whitaker added, "Fundamentally, the Mueller investigation has a very defined scope."

Mueller was appointed in May 2017, shortly after President Trump fired FBI Director James Comey, to conduct an investigation into "any links and/or coordination between the Russian government" and individuals associated with then-candidate Trump's presidential campaign, as well as any matters arising "directly" from the probe.

Asked by Fox News if the Justice Department would investigate witnesses who Republicans have accused of misleading Congress -- including Comey and fired FBI agent Peter Strzok -- Whitaker responded, "We take very seriously lying to Congress. If referrals are made by committees, we would investigate."

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In the course of the investigation, Mueller has secured criminal convictions of numerous former Trump advisers -- including his onetime campaign manager Paul Manafort and National Security Adviser Michael Flynn -- but none of the charges directly pertained to a criminal conspiracy with Russian officials related to efforts to meddle in the 2016 elections.

For example, the special counsel's 24-page indictment unsealed on Friday alleged that Stone worked to obstruct the House Intelligence Committee’s investigation into Russian interference by making false statements to the committee, denying he had records sought by the committee and persuading a witness to provide false testimony.

According to the indictment, Stone told an associate, Randy Credico, to do a "Frank Pentangeli’” when testifying before Congress -- a reference to a character in "The Godfather: Part II." Stone also told Credico, "I guarantee you you are the one who gets indicted for perjury if you’re stupid enough to testify.”

Stone has insisted he was joking, and the indictment does not charge Stone with conspiring with WikiLeaks, the anti-secrecy website that published emails of Democrats during the 2016 campaign, or with the Russian officers Mueller says hacked them.

Flynn, like former Trump foreign policy adviser George Papadopoulos, was charged only with lying to investigators after the Russia probe began. (Prosecutors maintained that they could have also secured convictions for procedural violations of the Foreign Agents Registration Act violations against Flynn as well)

Manafort's convictions related largely to bank and tax fraud.

Meanwhile, William Barr, Trump's nominee to replace Whitaker as attorney general on a full-time basis, sent written responses to questions from the Senate Judiciary Committee earlier Monday.

In his responses, Barr stressed he would not interfere with Mueller's investigation and that his previous memorandum critical of Mueller's authority did not necessarily reflect his current views.

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Barr also acknowleged he previously had spoken with Vice President Mike Pence about the Mueller investigation in 2017, but said he had provided no legal advice to the White House and denied that Pence had provided any classified information.

Barr, who served previously as attorney general in President George H.W. Bush's administration, appeared headed for confirmation in the Republican-controlled Senate.

Fox News' Jake Gibson and Catherine Herridge contributed to this report.