Mueller's appointment raised questions about whether he would ask Congress to step away from its investigation, or whether the dual track would complicate issues such as calling witnesses or obtaining documents.
The Justice Department named former FBI Director Robert Mueller as special counsel to investigate alleged Russian interference in the 2016 U.S. election and possible collusion between Trump's campaign and Moscow.
The White House pointed to Rosenstein's memo last week as justification for Trump's abrupt decision to dismiss Comey.
"This is the single greatest witch hunt of a politician in American history!"
A senior US senator said on Friday that he expects Congress' investigation of Russian Federation and the 2016 USA election to go ahead, even after the appointment of a special counsel, and said Congress has a broader mandate that extends to financial conflicts of interest.
The special counsel announcement was made by Deputy Attorney General Rod Rosenstein, who the White House initially credited for Trump's firing of Comey. Rosenstein said the Mueller appointment was "necessary in order for the American people to have full confidence in the outcome".
Trump has said he plans to nominate a new Federal Bureau of Investigation director soon, and that had been expected before his departure.
Democrats - and many Republicans - had been eager to hear from Comey after reports emerged this week that Trump may have urged the then-FBI director to drop an investigation into former national security adviser Michael Flynn.
Senators said that Rosenstein steered clear of specifics while making clear that Mueller has wide latitude to pursue the investigation wherever it leads, including potentially criminal charges.
Mueller, a former federal prosecutor at the Justice Department, was confirmed as FBI director days before the September 11, 2001, attacks that would ultimately shape his tenure. He was so valued that President Barack Obama asked him to stay on two years longer than his 10-year term.More news: Senators Query FCC Over Manhandling of Reporter After Meeting
Unlike his unusually candid predecessor Comey, Mueller is a notoriously tight-lipped investigator.
House Speaker Paul Ryan said the appointment was consistent with his goal of ensuring that "thorough and independent investigations are allowed to follow the facts wherever they may lead".
Trump's terse denial followed reports by Reuters and other media about a memo written by Comey alleging that Trump made the request to close down the investigation into Michael Flynn and Russian Federation in February.
The newspaper cites the White House's official written account of the Oval Office meeting.
Melania Trump is accompanying President Donald Trump on his inaugural overseas trip, a four-country, five-stop tour that begins Friday. "The Congress has a broader oversight responsibility than just whether crimes have been committed", Senator Ron Wyden, the ranking Democrat on the Senate Finance Committee and a senior member of the Senate Intelligence Committee, said during a round-table meeting with Reuters.
Trump had said Thursday he was "very close" to naming a replacement and that former Connecticut Sen.
"This shuts the whole thing down", said one Republican source, speaking on Congressional efforts to investigate Comey's discussions with Trump. Joe Lieberman was among his top choices.
The Wednesday decision to name former FBI Director Robert Mueller, an apolitical outsider, to oversee the case seemed meant to restore public faith in an independent Justice Department following a series of headache-inducing headlines.
The triple whammy has left Trump aides dazed and wondering about the future of his young presidency.