Senate Republicans could confirm a new AG on a simple party-line vote.
Democrats warned against interference in the probe. The move has sparked concern that Whitaker would end or hamper the investigation. Trump told associates that he felt that Whitaker would be "loyal" and would not have recused himself from the Russian Federation probe as Sessions had done, according to two Republicans close to the White House not authorized to speak publicly about private conversations. Whitaker, a former Republican politician, has publicly called for limits on the Mueller probe.
In an op-ed in August past year he publicly urged Deputy Attorney General Rod Rosenstein - who oversees the probe - to "limit the scope of his investigation to the four corners of the order appointing him special counsel".
As deputy attorney general, Rosenstein is responsible for the day-to-day operations of the Justice Department, including the activities of the country's USA attorneys. "Deputy Attorney General Rosenstein must be allowed to protect the Special Counsel and insulate the investigation from interference by the White House".
When asked whether Whitaker would now assume control over the Mueller investigation, U.S. Justice Department spokesperson Sarah Flores said Whitaker would be "in charge of all matters" under the purview of the department.More news: How will Jeff Sessions' ouster affect the Mueller probe?
Mueller declined to comment, according to his spokesman, Peter Carr.
Whitaker, in a Justice Department statement released on Wednesday evening said, "I am committed to leading a fair department with the highest ethical standards, that upholds the rule of law, and seeks justice for all Americans". He added that it had "been a privilege" to work under Sessions.
"I could fire everybody right now, but I don't want to stop it because politically I don't like stopping it", Mr Trump told a White House news conference.
Rosenstein has several severe conflicts of interest when it comes to the Mueller probe and the Obama administration's "spygate" efforts against President Trump and his associates.
There are still questions about Whitaker's ability to take over as Attorney General, due to the fact that he served as Session's chief of staff and was not confirmed by the Senate.More news: Women candidates make history in U.S. 2018 midterm elections
Gustoff said he, Whitaker and Hagenow founded their law firm with common conservative beliefs and the goal of serving their faith, families and Iowans rather than exclusively to make money.
In addition to Sessions' ouster, Democrats are also interested in looking into Mr. Trump's tax returns, and global business dealings.
Earlier on Wednesday, Mr Trump denied he would shut down Mr Mueller's team, but still labelled the investigation an illegal "witch hunt" that had spent "millions" of dollars.
He ran for Iowa state treasurer in 2002, years before making his failed 2014 U.S. Senate.
Mueller, who has been negotiating with Trump's lawyers about interviewing the president, is expected to produce a written report for the Justice Department that explains the findings, though it's not clear how much will be public.More news: Paul Pogba says beating Juventus was unusual
Last November, Whitaker penned a CNN op-ed claiming that the Robert Mueller investigation was going too far by digging into the president's financial records.