Rosenstein briefed the US Senate just one day after he turned the political world on its head by appointing a special counsel to investigate possible collusion between the campaign of President Donald Trump and Russian officials meddling in last year's election.
Mueller was named as special counsel on Wednesday, one day after a report surfaced that Trump had requested ex-FBI Director James Comey end any investigations involving National Security Adviser Michael Flynn's contacts with Russian Federation.
Trump also suggested that former United States presidents Barack Obama and Bill Clinton had committed acts that should have been investigated by a special prosecutor.
Lawmakers were still picking through the fallout of Wednesday's stunning announcement by deputy Attorney General Rod Rosenstein that he appointed Mueller to direct the special investigation into ties between Trump aides and Russian Federation.
"Based upon the unique circumstances, the public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command", Rosenstein said in a statement on Wednesday.
It followed the revelation Tuesday that fired FBI Director James Comey had written in a memo that Trump, in a February meeting in the Oval Office, had asked him to end an investigation into former national security adviser Michael Flynn.
Trump said in a statement after the Justice Department announcement he looked forward to a quick resolution.
Rosenstein denied media reports from last week that Comey had asked him for additional resources for his investigation before Trump fired him.
Capping days of political drama in Washington, the move came as pressure mounted in Congress for an independent probe into ties between Trump's campaign and Moscow, which U.S. intelligence chiefs say interfered to tilt the election in the Republican's favour.More news: Trump says he's 'very close' to naming a new Federal Bureau of Investigation director
Trump has insisted at times that the decision was his alone, but he also has pointed - as recently as Thursday - to the "very strong" recommendation from Rosenstein. Earlier this week, press secretary Sean Spicer told reporters that there was "no need" for such an appointment, adding: "You have two Senate committees that are looking into this, [and] the Federal Bureau of Investigation is conducting their own review".
Q. What will Mueller do as special counsel?
The term is used somewhat interchangeably with "special prosecutor", but the latter is outdated.
Faso, R-Kinderhook, who represents New York's 19th Congressional District, said Thursday that the Justice Department's selection of Mueller, a former FBI director, ensures a credible investigation.
The No. 2 Senate Republican, John Cornyn of Texas, said he is supportive of investigations in Congress but expressed concern about the "proliferation" of hearings.
The appointment came amid a growing Democratic outcry for someone outside the Justice Department to handle the politically charged investigation.
Deputy Attorney General Rod Rosenstein knew President Trump planned to fire FBI Director Jim Comey before he sat down to write a memo criticizing Comey's conduct. Trump said in a tweet.
Ryan held a news conference Thursday, in which he repeatedly attempted to steer the conversation back to House Republicans' legislative priorities.
Rosenstein said the Mueller appointment was "necessary in order for the American people to have full confidence in the outcome". The action was a concession by the Trump administration to Democratic demands for the investigation to be run independently of the Justice Department.