William Barr, who previously served as attorney-general under George HW Bush, told his Senate confirmation hearing that it was "vitally important the special counsel be allowed to complete his investigation".
If confirmed, Barr would take over supervision of the probe from the No. 2 Justice Department official, Rod Rosenstein, who has overseen the effort since the previous attorney general, Jeff Sessions, recused himself, a decision Trump repeatedly criticized. The nominee said he has known Mueller "personally and professionally for 30 years", having worked together at the Justice Department.
The remarks attempt to address concerns that Trump intends for Barr to act as a firewall between him and the justice department or to sink the Mueller investigation.
Given Mr Barr's long history of government service and the fact that Republicans hold a majority in the Senate, successful confirmation seems fairly certain. If and when he becomes the attorney general, Barr will assume oversight of the probe from Whitaker.
Donald Trump's nominee for attorney-general today said he did not believe that the investigation into Russian election interference was a "witch hunt", as the president has claimed.
He said he raised his concerns at a lunch a year ago with the deputy attorney general, Rod Rosenstein, who appointed Mueller and oversees his work.
In another key moment, Mr Barr was asked about former Attorney General Jeff Sessions' self-recusal from the Russian Federation inquiry, a decision that infuriated Mr Trump.
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He repeatedly said special counsel Robert Mueller must be allowed to complete his inquiry into whether the Trump campaign colluded with an alleged Russian plot to influence the 2016 U.S. presidential election. Dianne Feinstein, D-Calif.,(R) questions Attorney General nominee William Barr during a Senate Judiciary Committee hearing on Capitol Hill in Washington, Jan. 15, 2019. Rosenstein did not respond and was "sphinx-like", Barr recalled.
What is Barr's view of presidential pardoning power?
Barr will tell senators the Justice Department can not allow people to flout America's legal system by "crashing in through the back door".
Democrats - and perhaps Republicans - are sure to have questions about Barr's approach to Mueller, especially since Barr has been critical of the Mueller probe in the past.
Barr also sent the memo to White House lawyers and discussed it with Trump's personal attorneys and a lawyer who represents Trump's son-in-law, Jared Kushner.
The Justice Department will then be able to provide the report to Congress and possibly the public.
Barr also said it was "very important" that Congress and the public be informed of what Mueller investigated and concluded.
"President Trump has sought no assurances, promises, or commitments from me of any kind, either express or implied, and I have not given him any, other than that I would run the department with professionalism and integrity", Barr said. He said presidents can not be criminally investigated for actions they are permitted to take under the Constitution, such as firing officials who work for them, just because of a subjective determination that they may have had a corrupt state of mind.