The president was referring to the fact that Rosenstein drafted a memo on why FBI Director James Comey should be fired, and that special counsel Mueller is reportedly including the firing of Comey within the scope of his investigation, as an instance of possible obstruction of justice.
Wide consensus among the USA intelligence community asserts that Russian President Vladimir Putin sought to undermine America's electoral process.
Housing and Urban Development Secretary Ben Carson said Friday that he believes special counsel Robert Mueller should be given a chance to do his job, but added that "there's nothing to find" in relation to the Donald Trump's campaign and Russian meddling in the 2016 election.
The Trump administration initially said Mr Rosenstein's letter was the reason the President fired Mr Comey on May 9, but Mr Trump later said he did so because of the "Russia thing". The attorney general was at a White House meeting when the notification came from Rosenstein, prompting the enraged President to scold the attorney general for the turn of events.
Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, said she was "increasingly concerned" that Mr Trump will sack both Mr Mueller and Mr Rosenstein.
But Republicans also worry that Mr. Trump is giving Mueller more material to investigate all the time.
The Democratic National Committee, in a statement Friday, said that Rosenstein, who has authority over Mueller, needs to recuse himself from the Russian Federation investigation and that control of the investigation should not be given to another presidential appointee.
Kenneth Starr, the independent counsel in the Whitewater and Monica Lewinsky investigation that led to the impeachment of President Bill Clinton, wrote in an op-ed column in the Washington Post, "Mueller should be allowed to do his work unhindered and unimpeded". "Americans should be skeptical about anonymous allegations".
"You begin to wonder if is going to be a domino effect here where it is just one person after another", said Andrew Graham, a longtime Maryland defense lawyer who worked with Rosenstein.
Mr Comey told a Senate panel last week he believed Mr Trump fired him to undermine the FBI's Russian Federation probe and testified that the President directed him in February to drop an investigation into former national security adviser Michael Flynn in relation to the Russian Federation matter.
It was not clear whether the president was basing his tweet on direct knowledge, or on reports this week that special counsel Robert Mueller is examining whether he obstructed justice by firing Mr Comey last month amid the Russian Federation investigation. A Justice Department spokesman didn't rule out that possibility Friday, saying, "As the Deputy Attorney General has said numerous times, if there comes a point where he needs to recuse, he will". They are building a case for firing Mueller.
A Trump's transition official confirmed the lawyer's internal order, which was sent on Thursday.
Yet Trump's angry tweets on Friday underscored the near-impossible challenge his advisers and legal team have in trying to get him to avoid weighing in on an active probe.
He also has millions of followers on his official Facebook pages.
Trump's personal lawyer, Michael Cohen, also has retained an attorney to represent him. He has already been subpoenaed by the House of Representatives intelligence committee.
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