A Kremlin spokesman, Dmitry Peskov, on Thursday called Mueller's investigation a "headache" for USA authorities but said it "has nothing to do with us", and he declined to comment on Sessions' departure.
Democratic Senator Richard Blumenthal of CT also criticized Whitaker's appointment.
Des Moines attorney Guy Cook, a Democrat who has known Whitaker for years, called him a clear thinker and a "no-nonsense guy who is not to be underestimated".
'Nor has a President ever before appointed an acting attorney general who is on record describing the means by which the President could curtail an ongoing investigation of the President's conduct'.
Le'Veon Bell back in Pittsburgh but no word on meeting team
But most people don't take the time to simply read between the lines and that's clearly on them. Just about everybody has an opinion on my life & anxious about what I'm doing.
Democrats see this latest move as an attempt to do just that.
Trump blamed the recusal for the appointment of Mueller, who took over the Russian Federation investigation two months later and began examining whether Trump's hectoring of Sessions was part of a broader effort to obstruct the probe.
After recusing himself from the Russian Federation probe, the staunchly conservative Sessions spent his time ramping up efforts to combat violent gangs, drug use and illegal immigration - all key components of Trump's law-and-order agenda.
Her words were echoed by Democratic party Senate leader Chuck Schumer, who added: "Clearly, the president has something to hide."
Mr Whitaker has publicly criticised Mr Mueller's conduct several times since the inquiry began in May previous year and taken the side of Mr Trump, who has dismissed it... He had frequently publicly castigated Sessions for recusing himself past year from the case.
"Trump's actions are being compared with those of U.S. President Richard Nixon in one of the most controversial episodes of the Watergate scandal, the Saturday Night Massacre", said organizers.
Trump firing Sessions is a 'break the glass moment — Richard Blumenthal
He recused himself the next day, saying it would be inappropriate to oversee an investigation into a campaign he was part of. Sessions had recused himself from Mueller's investigation , leaving oversight to Deputy Attorney General Rod Rosenstein.
"At your request, I am submitting my resignation", Mr Sessions said in the first line of a letter released by the Department of Justice.
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.
That left Rosenstein overseeing the investigation, and he named Mueller as special counsel.
Under the special counsel regulation, Whitaker has the power to block any "investigative or procedural step" Mueller recommends, such as bringing an indictment or subpoena, if he determines it to be "inappropriate or unwarranted under established Departmental practices".
One of the exceptions, Senator Susan Collins, said non-interference in the Mueller probe was "imperative".
The special counsel has also been investigating whether Mr Comey's firing amounted to obstruction of justice.
Democrats Will Likely Reclaim Control Of The House Of Representatives
The House of Representatives has flipped from Republican control into the hands of the Democrats, US networks projected . Women powered the Democrats' victories across the country as well, driving the highest gender gap in modern history.
In addition to Sessions' ouster, Democrats are also interested in looking into Mr. Trump's tax returns, and global business dealings.