But President Trump emphasised again that he did not know Mr Whitaker.
Senator Susan Collins on Friday said she wants the Senate to debate placing restrictions on Trump's ability to remove Mueller.
Thanking Sessions for his service, Romney said that it was "imperative that the important work of the Justice Department continues, and that the Mueller investigation proceeds to its conclusion unimpeded".
U.S. Senate Majority Leader Mitch McConnell addresses a news conference after the Senate voted to confirm the Supreme Court nomination of Judge Brett Kavanaugh at the U.S. Capitol in Washington, Oct. 6, 2018. Likewise, as Chief, I did not know Mr Whitaker except primarily as he traveled with AG Sessions.
But in an interview with "Fox & Friends" on October 11, the president was asked to respond to a report in the Washington Post that he had talked to Whitaker - at the time Sessions's chief of staff - about replacing the attorney general.
He added, "I'm not saying he's indicting the president". The new position handed him oversight of Mueller's investigation into possible ties between Russian Federation and Trump's 2016 presidential campaign. But instead of announcing that Rosenstein would assume the position of Acting Attorney General, Trump turned to a passionate loyalist to take charge of overseeing an investigation Whitaker has publicly called a "witch hunt."
There have also been reports about Whitaker's past comments questioning the power and reach of the federal judiciary, and about his ties to an invention-promotion company that was accused of misleading consumers.
Once a USA attorney for the Southern District of Iowa, Whitaker also served as a legal commentator at CNN until he joined the DOJ in September 2017. Chuck Grassley, R-Iowa, and U.S. Ambassador to China Terry Branstad were among those who thought "very highly" of Whitaker.
"Matt Whitaker is a very smart man, he is a very respected man in the law enforcement community, top of the line", Trump said.
Whitaker and White House chief of staff John Kelly developed a close relationship too.
"The left is trying to sow this theory that essentially Russians interfered with the USA election, which has been proven false", Whitaker said in an interview with a conservative Christian broadcaster.
"We thank Attorney General Jeff Sessions for his service and wish him well!" Trump "threw Whitaker into an immediate political and legal storm", with the unexpectedly quick departure of Sessions.
In an email to Department of Justice staff on Friday, Whitaker vowed to lead "a fair Department with the highest ethical standards, that upholds the rule of law, and seeks justice for all Americans".
Slogans included "Hands off Mueller" and "Nobody's above the law".
The president has repeatedly said he doesn't watch CNN.
Before the resignation of Attorney General Jeff Sessions was turned in this past Wednesday, very few people had heard of his temporary replacement, Matthew Whitaker. When asked whether he required a "Levitical or New Testament" view of justice, Whitaker specified the New Testament. He now has a concrete enemy in Congress to do battle with, and he gets to make the Mueller investigation a partisan fight between him and Congressional Democrats, which is where he thrives.
Democrats winning back the House isn't entirely bad for Trump.