After Trump fired FBI Director James Comey, Trump said that Comey had told him three times that he was not under investigation. Comey later testified that he'd authorized a friend to disclose to the media his notes on conversations with Trump about the investigation, in hopes that it would lead the Justice Department to name a special counsel.
Dianne Feinstein, top Democrat on the Senate Judiciary Committee, said she was "increasingly concerned" that Trump will fire both Mueller and Rosenstein.
"That is a great, great team of complete professionals, so let's let him do his job", former independent counsel Kenneth Starr, who investigated President Bill Clinton in the 1990s, told ABC News.
Mr Comey, who had been leading one of several Russian Federation inquiries, testified to Congress last week that Mr Trump had pressurised him to drop the investigation into former National Security Adviser Michael Flynn.
The Post reported that the obstruction of justice investigation of the president began days after James Comey was sacked as the FBI Director on May 9. The order also covers separate inquiries into several key Trump associates including former National Security Adviser Michael Flynn, campaign adviser Paul Manafort, foreign policy aide Carter Page and outside adviser Roger Stone. Trump lashed out on Twitter, calling the news a "witch hunt" and a "phony story".
In a tweet early Thursday, Trump said: "They made up a phony collusion with the Russians story, found zero proof, so now they go for obstruction of justice on the phony story".
Donald Trump has also regularly bashed media reports using unnamed officials and sources.
Mueller has assembled a high-powered team of top investigators and leading experts, including seasoned attorneys who've represented major American companies in court and who have worked on cases ranging from Watergate to the Enron fraud scandal. He's a leaker, ' Trump said at a press conference referencing Comey, before pivoting to trade deficits and other geographic regions that could pose a problem to the United States.
Modi to meet Trump on June 25-26
Apart from ways to enhance trade and business cooperation, the two leaders are expected to discuss defence ties. The two leaders have spoken over phone at least thrice since the latter assumed office.
Mr. Mueller's investigation appeared to be reaching a circle of current and former officials.
The latest development was first carried in the Washington Post.
Trump, alluding to Deputy Attorney General Rod Rosenstein, wrote that he is being "investigated for firing the FBI Director by the man who told me to fire the FBI Director!"
Days after Comey was abruptly ousted, Rosenstein appointed Robert Mueller as special counsel to investigate Russian involvement in the 2016 presidential election and possible collusion with the Trump campaign.
Trump demonstrated Friday morning that the Russian Federation probe continues to consume his attention, tweeting a stream of messages decrying the controversy.
A spokesman for Mr Mueller's team declined to comment on Wednesday. Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal.
Trump, in a most revealing interview with NBC News anchor Lester Holt, had said he had the handling of "the Russian thing" in mind when he decided on his own to fire Comey. As for Comey, he remains a shrewd and calculating defender of the rule of law and its instruments, positioned to defend them against a president he sees as an unprincipled political opportunist in a highly unsafe time for the country.
Marc Kasowitz, Trump's personal lawyer, said Comey's testimony vindicated that Trump wasn't under investigation by the FBI.