President Trump and special counsel Robert S. Mueller III. (Jabin Botsford; Win McNamee/The Washington Post; Getty Images)

The chairman of the House Intelligence Committee said Sunday that special counsel Robert S. Mueller III was making a “mistake” by not demanding that President Trump testify as part of his investigation, which by many accounts may soon be nearing its end.

Speaking on NBC’s “Meet the Press,” Rep. Adam B. Schiff (D-Calif.) acknowledged that it might be expedient for Mueller to avoid subpoenaing Trump’s testimony because the president could fight it and Mueller’s new boss, Attorney General William P. Barr, might oppose such a move.

“But I do think ultimately it’s a mistake because probably the best way to get the truth would be to put the president under oath,” Schiff said. “As he’s made plain in the past, he feels it’s perfectly fine to lie to the public. After all, he has said, ‘It’s not like I’m talking before a magistrate.’ Well, maybe he should talk before a magistrate.”

Schiff also said he is deferring to Mueller on whether Erik Prince, a former Navy SEAL who created the controversial Blackwater security company, lied to Congress about his involvement in the Trump campaign.

The House Intelligence Committee spoke with Prince in 2017 about his meeting in January that year with Kirill Dmitriev, head of the Russian Direct Investment Fund, that the United Arab Emirates organized in the Seychelles. Prince presented the meeting to congressional investigators as a series of coincidences and insisted to the committee that he played no formal or informal role in Trump’s campaign or transition team.

But it is an August 2016 meeting in Trump Tower, which Prince admitted to participating in during an interview with Al Jazeera last week but never disclosed to the Intelligence panel, that has revived suspicions that Prince lied to Congress under penalty of perjury.

In the Al Jazeera interview, Prince at first said he did not disclose the August meeting to investigators because “I don’t believe I was asked that question.” He later said he “certainly” had told investigators about it, despite no mention of it in the public transcript. Prince tried to explain that discrepancy by saying, “I don’t know if they got the transcript wrong.” Members of the panel were not convinced by his contradicting explanations.

“He’s certainly not telling the truth in that interview. There’s nothing wrong with our transcript. . . . He did not disclose that meeting to our committee,” Schiff said. “So his, you know, interview certainly looks inconsistent with his testimony.”

But Schiff stopped short of accusing Prince of perjury, leaving those questions to Mueller.

“Bob Mueller will have to make the decision about whether that rises to a level of deliberate falsehood,” Schiff said. “But we had questions at the time of his testimony about his candor and his, how forthcoming he was. And those questions have only been heightened now.”

A lawyer for Prince did not immediately respond to a request for comment.

Schiff is not the only member of the Intelligence Committee who says that, in general, Prince was not truthful with investigators.

“He beyond strained credibility in the interview,” panel member Mike Quigley (D-Ill.) said when reached for comment Saturday. “He’s full of it; he’s always been full of it. . . . You can’t trust him.”

“Opinion only, but I think he is a liar,” panel member Jackie Speier (D-Calif.) said.

Lying to Congress is a crime that has resulted in legal charges against Trump’s longtime friend Roger Stone and his former lawyer and fixer Michael Cohen, who pleaded guilty to the charge and will soon begin a three-year prison term for that and financial crimes.

Cohen appeared on Capitol Hill four times in the last two weeks, attempting to correct the record after misleading lawmakers during 2017 interviews before the House and Senate Intelligence panels and to accuse Trump of what he said were financial and other crimes.

Yet after several rounds of open and closed testimony, lawmakers say they still aren’t sure whether Cohen is telling the whole truth.

He said during his public testimony that he had “never asked for, nor would I accept, a pardon from President Trump.” But following his closed-door testimony with the House Intelligence Committee, Cohen’s lawyer Lanny Davis said Cohen had directed a previous attorney, Stephen Ryan, to ask about a pardon after Trump’s representatives publicly “dangled” the idea.

Trump weighed in on the subject last week in a tweet, saying that Cohen “directly asked me for a pardon.”

“I said NO,” Trump’s tweet continued. “He lied again! He also badly wanted to work at the White House. He lied!”

Speaking on CBS’s “Face the Nation,” Sen. John Neely Kennedy (R-La.) said, “I don’t blame Cohen for asking” for the pardon, even if doing so was “inappropriate.” But he said Cohen’s swirling statements were clear proof that he was still lying to lawmakers: “If he’s breathing, he’s lying.”

Democrats have acknowledged that Cohen’s testimony is too shaky to build a case around without corroboration.

“I don’t think in terms of making the case to the public, and here we’re not making the case to a jury, about what took place, that we can rely solely on the testimony of Michael Cohen,” Schiff said, noting that the sometimes conflicting statements from Cohen and his lawyers during and after open and closed-door testimony reminded him of the shifting narratives of the president.

“Those transcripts will be made public,” Schiff said of Cohen’s two days of closed-door testimony with the House Intelligence Committee. “The public can evaluate his credibility themselves.”

Earlier this year, the committee sent to Mueller all the transcripts from its GOP-led investigation of Russian interference in the 2016 election. In an interview Sunday, Cohen’s lawyer Davis said they “have a great deal of respect and appreciation for Mr. Schiff, and Mr. Cohen testified truthfully.”

In recent days, Republican lawmakers have accused Cohen of planning his testimony with Schiff, pointing to meetings that Intelligence Committee staffers held with him before his interviews on Capitol Hill. A spokesman for Schiff last week described those meetings as routine “proffer sessions.” Cohen’s lawyer said he went through similar preliminary sessions with the Senate Intelligence Committee and had offered to meet with House Republicans, including Jim Jordan of Ohio, but those gestures were ignored.

“I asked to meet with Mr. Jordan with Mr. Cohen before the House Oversight hearing twice, and Mr. Jordan never responded. Then I asked to and met with his staff before, to brief them,” Davis said.

A spokeswoman for Jordan said Sunday that while GOP staff of the Oversight Committee did meet with Davis in January to go over what Cohen could and could not discuss — and later requested Cohen first agree to a closed-door briefing in advance of his public testimony — the only thing Davis offered Jordan in February was a meet-and-greet with Cohen, on the condition that he would answer no questions.